Incorrect MIP Optimality
AnsweredI have two MIP models original.lp and modified.lp which differ only in the two additional constraints of modified.lp. Thus, the objective value of modified.lp should be larger or equal to that of original.lp. However, this is not the case. Moreover, by solving a symmetric MIP, I can verify that the value of modified.lp is correct. Why is OPT(modified.lp) = -0.0609 < -0.05505 = OPT(original.lp) even though Gurobi claims having found the optimal solution in both cases?
original.lp
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
pixel_13_22 + 0 abs_v_x_13_22 + 0 abs_v_y_13_22 + 0 pixel_12_22
+ 0 abs_v_x_12_22 + 0 abs_v_y_12_22 + 0 pixel_14_22 + 0 abs_v_x_14_22
+ 0 abs_v_y_14_22 - pixel_13_21 + 0 abs_v_x_13_21 + 0 abs_v_y_13_21
+ 0 pixel_13_23 + 0 abs_v_x_13_23 + 0 abs_v_y_13_23
Subject To
interpolation_13_22: top_left_13_22 + top_right_13_22 + bottom_left_13_22
+ bottom_right_13_22 = 1
interpolation_12_22: top_left_12_22 + top_right_12_22 + bottom_left_12_22
+ bottom_right_12_22 = 1
interpolation_14_22: top_left_14_22 + top_right_14_22 + bottom_left_14_22
+ bottom_right_14_22 = 1
interpolation_13_21: top_left_13_21 + top_right_13_21 + bottom_left_13_21
+ bottom_right_13_21 = 1
interpolation_13_23: top_left_13_23 + top_right_13_23 + bottom_left_13_23
+ bottom_right_13_23 = 1
flow_p_x_12_22: v_x_13_22 - v_x_12_22 <= 0.01
flow_n_x_12_22: - v_x_13_22 + v_x_12_22 <= 0.01
flow_p_y_12_22: v_y_13_22 - v_y_12_22 <= 0.01
flow_n_y_12_22: - v_y_13_22 + v_y_12_22 <= 0.01
flow_p_x_14_22: v_x_13_22 - v_x_14_22 <= 0.01
flow_n_x_14_22: - v_x_13_22 + v_x_14_22 <= 0.01
flow_p_y_14_22: v_y_13_22 - v_y_14_22 <= 0.01
flow_n_y_14_22: - v_y_13_22 + v_y_14_22 <= 0.01
flow_p_x_13_21: v_x_13_22 - v_x_13_21 <= 0.01
flow_n_x_13_21: - v_x_13_22 + v_x_13_21 <= 0.01
flow_p_y_13_21: v_y_13_22 - v_y_13_21 <= 0.01
flow_n_y_13_21: - v_y_13_22 + v_y_13_21 <= 0.01
flow_p_x_13_23: v_x_13_22 - v_x_13_23 <= 0.01
flow_n_x_13_23: - v_x_13_22 + v_x_13_23 <= 0.01
flow_p_y_13_23: v_y_13_22 - v_y_13_23 <= 0.01
flow_n_y_13_23: - v_y_13_22 + v_y_13_23 <= 0.01
v_x_top_left_min_13_22: top_left_13_22 = 1 -> - v_x_13_22 <= 0.1
v_x_top_left_max_13_22: top_left_13_22 = 1 -> v_x_13_22 <= 0
v_y_top_left_min_13_22: top_left_13_22 = 1 -> - v_y_13_22 <= 0.1
v_y_top_left_max_13_22: top_left_13_22 = 1 -> v_y_13_22 <= 0
v_x_top_right_min_13_22: top_right_13_22 = 1 -> - v_x_13_22 <= 0
v_x_top_right_max_13_22: top_right_13_22 = 1 -> v_x_13_22 <= 0.1
v_y_top_right_min_13_22: top_right_13_22 = 1 -> - v_y_13_22 <= 0.1
v_y_top_right_max_13_22: top_right_13_22 = 1 -> v_y_13_22 <= 0
v_x_bottom_left_min_13_22: bottom_left_13_22 = 1 -> - v_x_13_22 <= 0.1
v_x_bottom_left_max_13_22: bottom_left_13_22 = 1 -> v_x_13_22 <= 0
v_y_bottom_left_min_13_22: bottom_left_13_22 = 1 -> - v_y_13_22 <= 0
v_y_bottom_left_max_13_22: bottom_left_13_22 = 1 -> v_y_13_22 <= 0.1
v_x_bottom_right_min_13_22: bottom_right_13_22 = 1 -> - v_x_13_22 <= 0
v_x_bottom_right_max_13_22: bottom_right_13_22 = 1 -> v_x_13_22 <= 0.1
v_y_bottom_right_min_13_22: bottom_right_13_22 = 1 -> - v_y_13_22 <= 0
v_y_bottom_right_max_13_22: bottom_right_13_22 = 1 -> v_y_13_22 <= 0.1
v_x_top_left_min_12_22: top_left_12_22 = 1 -> - v_x_12_22 <= 0.1
v_x_top_left_max_12_22: top_left_12_22 = 1 -> v_x_12_22 <= 0
v_y_top_left_min_12_22: top_left_12_22 = 1 -> - v_y_12_22 <= 0.1
v_y_top_left_max_12_22: top_left_12_22 = 1 -> v_y_12_22 <= 0
v_x_top_right_min_12_22: top_right_12_22 = 1 -> - v_x_12_22 <= 0
v_x_top_right_max_12_22: top_right_12_22 = 1 -> v_x_12_22 <= 0.1
v_y_top_right_min_12_22: top_right_12_22 = 1 -> - v_y_12_22 <= 0.1
v_y_top_right_max_12_22: top_right_12_22 = 1 -> v_y_12_22 <= 0
v_x_bottom_left_min_12_22: bottom_left_12_22 = 1 -> - v_x_12_22 <= 0.1
v_x_bottom_left_max_12_22: bottom_left_12_22 = 1 -> v_x_12_22 <= 0
v_y_bottom_left_min_12_22: bottom_left_12_22 = 1 -> - v_y_12_22 <= 0
v_y_bottom_left_max_12_22: bottom_left_12_22 = 1 -> v_y_12_22 <= 0.1
v_x_bottom_right_min_12_22: bottom_right_12_22 = 1 -> - v_x_12_22 <= 0
v_x_bottom_right_max_12_22: bottom_right_12_22 = 1 -> v_x_12_22 <= 0.1
v_y_bottom_right_min_12_22: bottom_right_12_22 = 1 -> - v_y_12_22 <= 0
v_y_bottom_right_max_12_22: bottom_right_12_22 = 1 -> v_y_12_22 <= 0.1
v_x_top_left_min_14_22: top_left_14_22 = 1 -> - v_x_14_22 <= 0.1
v_x_top_left_max_14_22: top_left_14_22 = 1 -> v_x_14_22 <= 0
v_y_top_left_min_14_22: top_left_14_22 = 1 -> - v_y_14_22 <= 0.1
v_y_top_left_max_14_22: top_left_14_22 = 1 -> v_y_14_22 <= 0
v_x_top_right_min_14_22: top_right_14_22 = 1 -> - v_x_14_22 <= 0
v_x_top_right_max_14_22: top_right_14_22 = 1 -> v_x_14_22 <= 0.1
v_y_top_right_min_14_22: top_right_14_22 = 1 -> - v_y_14_22 <= 0.1
v_y_top_right_max_14_22: top_right_14_22 = 1 -> v_y_14_22 <= 0
v_x_bottom_left_min_14_22: bottom_left_14_22 = 1 -> - v_x_14_22 <= 0.1
v_x_bottom_left_max_14_22: bottom_left_14_22 = 1 -> v_x_14_22 <= 0
v_y_bottom_left_min_14_22: bottom_left_14_22 = 1 -> - v_y_14_22 <= 0
v_y_bottom_left_max_14_22: bottom_left_14_22 = 1 -> v_y_14_22 <= 0.1
v_x_bottom_right_min_14_22: bottom_right_14_22 = 1 -> - v_x_14_22 <= 0
v_x_bottom_right_max_14_22: bottom_right_14_22 = 1 -> v_x_14_22 <= 0.1
v_y_bottom_right_min_14_22: bottom_right_14_22 = 1 -> - v_y_14_22 <= 0
v_y_bottom_right_max_14_22: bottom_right_14_22 = 1 -> v_y_14_22 <= 0.1
v_x_top_left_min_13_21: top_left_13_21 = 1 -> - v_x_13_21 <= 0.1
v_x_top_left_max_13_21: top_left_13_21 = 1 -> v_x_13_21 <= 0
v_y_top_left_min_13_21: top_left_13_21 = 1 -> - v_y_13_21 <= 0.1
v_y_top_left_max_13_21: top_left_13_21 = 1 -> v_y_13_21 <= 0
v_x_top_right_min_13_21: top_right_13_21 = 1 -> - v_x_13_21 <= 0
v_x_top_right_max_13_21: top_right_13_21 = 1 -> v_x_13_21 <= 0.1
v_y_top_right_min_13_21: top_right_13_21 = 1 -> - v_y_13_21 <= 0.1
v_y_top_right_max_13_21: top_right_13_21 = 1 -> v_y_13_21 <= 0
v_x_bottom_left_min_13_21: bottom_left_13_21 = 1 -> - v_x_13_21 <= 0.1
v_x_bottom_left_max_13_21: bottom_left_13_21 = 1 -> v_x_13_21 <= 0
v_y_bottom_left_min_13_21: bottom_left_13_21 = 1 -> - v_y_13_21 <= 0
v_y_bottom_left_max_13_21: bottom_left_13_21 = 1 -> v_y_13_21 <= 0.1
v_x_bottom_right_min_13_21: bottom_right_13_21 = 1 -> - v_x_13_21 <= 0
v_x_bottom_right_max_13_21: bottom_right_13_21 = 1 -> v_x_13_21 <= 0.1
v_y_bottom_right_min_13_21: bottom_right_13_21 = 1 -> - v_y_13_21 <= 0
v_y_bottom_right_max_13_21: bottom_right_13_21 = 1 -> v_y_13_21 <= 0.1
v_x_top_left_min_13_23: top_left_13_23 = 1 -> - v_x_13_23 <= 0.1
v_x_top_left_max_13_23: top_left_13_23 = 1 -> v_x_13_23 <= 0
v_y_top_left_min_13_23: top_left_13_23 = 1 -> - v_y_13_23 <= 0.1
v_y_top_left_max_13_23: top_left_13_23 = 1 -> v_y_13_23 <= 0
v_x_top_right_min_13_23: top_right_13_23 = 1 -> - v_x_13_23 <= 0
v_x_top_right_max_13_23: top_right_13_23 = 1 -> v_x_13_23 <= 0.1
v_y_top_right_min_13_23: top_right_13_23 = 1 -> - v_y_13_23 <= 0.1
v_y_top_right_max_13_23: top_right_13_23 = 1 -> v_y_13_23 <= 0
v_x_bottom_left_min_13_23: bottom_left_13_23 = 1 -> - v_x_13_23 <= 0.1
v_x_bottom_left_max_13_23: bottom_left_13_23 = 1 -> v_x_13_23 <= 0
v_y_bottom_left_min_13_23: bottom_left_13_23 = 1 -> - v_y_13_23 <= 0
v_y_bottom_left_max_13_23: bottom_left_13_23 = 1 -> v_y_13_23 <= 0.1
v_x_bottom_right_min_13_23: bottom_right_13_23 = 1 -> - v_x_13_23 <= 0
v_x_bottom_right_max_13_23: bottom_right_13_23 = 1 -> v_x_13_23 <= 0.1
v_y_bottom_right_min_13_23: bottom_right_13_23 = 1 -> - v_y_13_23 <= 0
v_y_bottom_right_max_13_23: bottom_right_13_23 = 1 -> v_y_13_23 <= 0.1
top_left_min_v_x_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 - 0.0729411765933037 abs_v_x_13_22 - pixel_13_22
<= -0.9960784316062927
top_left_max_v_x_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 + 0.0729411765933037 abs_v_x_13_22 - pixel_13_22
>= -0.9960784316062927
top_left_min_v_y_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 - 0.0729411765933037 abs_v_y_13_22 - pixel_13_22
<= -0.9960784316062927
top_left_max_v_y_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 + 0.0729411765933037 abs_v_y_13_22 - pixel_13_22
>= -0.9960784316062927
top_right_min_v_x_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.0545098036527634 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
top_right_max_v_x_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.0545098036527634 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
top_right_min_v_y_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.0545098036527634 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
top_right_max_v_y_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.0545098036527634 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_left_min_v_x_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
- 0.0117647051811218 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_left_max_v_x_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
+ 0.0117647051811218 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_left_min_v_y_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
- 0.0117647051811218 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_left_max_v_y_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
+ 0.0117647051811218 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_right_min_v_x_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.024705882370472 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_right_max_v_x_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.024705882370472 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_right_min_v_y_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.024705882370472 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_right_max_v_y_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.024705882370472 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
top_left_min_v_x_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 - 0.0607843138277531 abs_v_x_12_22
- pixel_12_22 <= -0.8784313797950745
top_left_max_v_x_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 + 0.0607843138277531 abs_v_x_12_22
- pixel_12_22 >= -0.8784313797950745
top_left_min_v_y_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 - 0.0607843138277531 abs_v_y_12_22
- pixel_12_22 <= -0.8784313797950745
top_left_max_v_y_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 + 0.0607843138277531 abs_v_y_12_22
- pixel_12_22 >= -0.8784313797950745
top_right_min_v_x_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
- 0.0729411765933037 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
top_right_max_v_x_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
+ 0.0729411765933037 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
top_right_min_v_y_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
- 0.0729411765933037 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
top_right_max_v_y_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
+ 0.0729411765933037 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_left_min_v_x_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0282352976500988 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_left_max_v_x_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0282352976500988 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_left_min_v_y_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0282352976500988 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_left_max_v_y_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0282352976500988 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_right_min_v_x_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0117647051811218 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_right_max_v_x_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0117647051811218 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_right_min_v_y_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0117647051811218 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_right_max_v_y_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0117647051811218 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
top_left_min_v_x_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.0545098036527634 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
top_left_max_v_x_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.0545098036527634 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
top_left_min_v_y_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.0545098036527634 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
top_left_max_v_y_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.0545098036527634 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
top_right_min_v_x_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.024705880926922 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
top_right_max_v_x_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.024705880926922 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
top_right_min_v_y_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.024705880926922 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
top_right_max_v_y_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.024705880926922 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_left_min_v_x_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.024705882370472 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_left_max_v_x_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.024705882370472 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_left_min_v_y_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.024705882370472 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_left_max_v_y_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.024705882370472 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_right_min_v_x_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.0243137254845351 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_right_max_v_x_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.0243137254845351 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_right_min_v_y_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.0243137254845351 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_right_max_v_y_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.0243137254845351 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
top_left_min_v_x_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.00627450803294778 abs_v_x_13_21
- pixel_13_21 <= -0.9960784316062927
top_left_max_v_x_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.00627450803294778 abs_v_x_13_21
- pixel_13_21 >= -0.9960784316062927
top_left_min_v_y_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.00627450803294778 abs_v_y_13_21
- pixel_13_21 <= -0.9960784316062927
top_left_max_v_y_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.00627450803294778 abs_v_y_13_21
- pixel_13_21 >= -0.9960784316062927
top_right_min_v_x_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.0199999988079071 abs_v_x_13_21
- pixel_13_21 <= -0.9960784316062927
top_right_max_v_x_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.0199999988079071 abs_v_x_13_21
- pixel_13_21 >= -0.9960784316062927
top_right_min_v_y_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.0199999988079071 abs_v_y_13_21
- pixel_13_21 <= -0.9960784316062927
top_right_max_v_y_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.0199999988079071 abs_v_y_13_21
- pixel_13_21 >= -0.9960784316062927
bottom_left_min_v_x_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
- 0.0729411765933037 abs_v_x_13_21 - pixel_13_21 <= -0.9960784316062927
bottom_left_max_v_x_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
+ 0.0729411765933037 abs_v_x_13_21 - pixel_13_21 >= -0.9960784316062927
bottom_left_min_v_y_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
- 0.0729411765933037 abs_v_y_13_21 - pixel_13_21 <= -0.9960784316062927
bottom_left_max_v_y_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
+ 0.0729411765933037 abs_v_y_13_21 - pixel_13_21 >= -0.9960784316062927
bottom_right_min_v_x_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 - 0.0545098036527634 abs_v_x_13_21 - pixel_13_21
<= -0.9960784316062927
bottom_right_max_v_x_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 + 0.0545098036527634 abs_v_x_13_21 - pixel_13_21
>= -0.9960784316062927
bottom_right_min_v_y_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 - 0.0545098036527634 abs_v_y_13_21 - pixel_13_21
<= -0.9960784316062927
bottom_right_max_v_y_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 + 0.0545098036527634 abs_v_y_13_21 - pixel_13_21
>= -0.9960784316062927
top_left_min_v_x_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
- 0.0117647051811218 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
top_left_max_v_x_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
+ 0.0117647051811218 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
top_left_min_v_y_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
- 0.0117647051811218 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
top_left_max_v_y_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
+ 0.0117647051811218 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
top_right_min_v_x_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
- 0.024705882370472 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
top_right_max_v_x_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
+ 0.024705882370472 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
top_right_min_v_y_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
- 0.024705882370472 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
top_right_max_v_y_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
+ 0.024705882370472 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_left_min_v_x_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
bottom_left_max_v_x_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_left_min_v_y_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
bottom_left_max_v_y_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_right_min_v_x_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_x_13_23
- pixel_13_23 <= -0.9960784316062927
bottom_right_max_v_x_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_x_13_23
- pixel_13_23 >= -0.9960784316062927
bottom_right_min_v_y_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_y_13_23
- pixel_13_23 <= -0.9960784316062927
bottom_right_max_v_y_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_y_13_23
- pixel_13_23 >= -0.9960784316062927
Bounds
pixel_13_22 <= 1
-0.1 <= v_x_13_22 <= 0.1
-0.1 <= v_y_13_22 <= 0.1
pixel_12_22 <= 1
-0.1 <= v_x_12_22 <= 0.1
-0.1 <= v_y_12_22 <= 0.1
pixel_14_22 <= 1
-0.1 <= v_x_14_22 <= 0.1
-0.1 <= v_y_14_22 <= 0.1
pixel_13_21 <= 1
-0.1 <= v_x_13_21 <= 0.1
-0.1 <= v_y_13_21 <= 0.1
pixel_13_23 <= 1
-0.1 <= v_x_13_23 <= 0.1
-0.1 <= v_y_13_23 <= 0.1
Binaries
top_left_13_22 top_right_13_22 bottom_left_13_22 bottom_right_13_22
top_left_12_22 top_right_12_22 bottom_left_12_22 bottom_right_12_22
top_left_14_22 top_right_14_22 bottom_left_14_22 bottom_right_14_22
top_left_13_21 top_right_13_21 bottom_left_13_21 bottom_right_13_21
top_left_13_23 top_right_13_23 bottom_left_13_23 bottom_right_13_23
General Constraints
abs_v_x_13_22: abs_v_x_13_22 = ABS ( v_x_13_22 )
abs_v_y_13_22: abs_v_y_13_22 = ABS ( v_y_13_22 )
abs_v_x_12_22: abs_v_x_12_22 = ABS ( v_x_12_22 )
abs_v_y_12_22: abs_v_y_12_22 = ABS ( v_y_12_22 )
abs_v_x_14_22: abs_v_x_14_22 = ABS ( v_x_14_22 )
abs_v_y_14_22: abs_v_y_14_22 = ABS ( v_y_14_22 )
abs_v_x_13_21: abs_v_x_13_21 = ABS ( v_x_13_21 )
abs_v_y_13_21: abs_v_y_13_21 = ABS ( v_y_13_21 )
abs_v_x_13_23: abs_v_x_13_23 = ABS ( v_x_13_23 )
abs_v_y_13_23: abs_v_y_13_23 = ABS ( v_y_13_23 )
End
modified.lp
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
pixel_13_22 + 0 abs_v_x_13_22 + 0 abs_v_y_13_22 + 0 pixel_12_22
+ 0 abs_v_x_12_22 + 0 abs_v_y_12_22 + 0 pixel_14_22 + 0 abs_v_x_14_22
+ 0 abs_v_y_14_22 - pixel_13_21 + 0 abs_v_x_13_21 + 0 abs_v_y_13_21
+ 0 pixel_13_23 + 0 abs_v_x_13_23 + 0 abs_v_y_13_23
Subject To
manual_1: v_x_13_21 = 0.08999999999999989
manual_2: v_y_13_21 = 0.1
interpolation_13_22: top_left_13_22 + top_right_13_22 + bottom_left_13_22
+ bottom_right_13_22 = 1
interpolation_12_22: top_left_12_22 + top_right_12_22 + bottom_left_12_22
+ bottom_right_12_22 = 1
interpolation_14_22: top_left_14_22 + top_right_14_22 + bottom_left_14_22
+ bottom_right_14_22 = 1
interpolation_13_21: top_left_13_21 + top_right_13_21 + bottom_left_13_21
+ bottom_right_13_21 = 1
interpolation_13_23: top_left_13_23 + top_right_13_23 + bottom_left_13_23
+ bottom_right_13_23 = 1
flow_p_x_12_22: v_x_13_22 - v_x_12_22 <= 0.01
flow_n_x_12_22: - v_x_13_22 + v_x_12_22 <= 0.01
flow_p_y_12_22: v_y_13_22 - v_y_12_22 <= 0.01
flow_n_y_12_22: - v_y_13_22 + v_y_12_22 <= 0.01
flow_p_x_14_22: v_x_13_22 - v_x_14_22 <= 0.01
flow_n_x_14_22: - v_x_13_22 + v_x_14_22 <= 0.01
flow_p_y_14_22: v_y_13_22 - v_y_14_22 <= 0.01
flow_n_y_14_22: - v_y_13_22 + v_y_14_22 <= 0.01
flow_p_x_13_21: v_x_13_22 - v_x_13_21 <= 0.01
flow_n_x_13_21: - v_x_13_22 + v_x_13_21 <= 0.01
flow_p_y_13_21: v_y_13_22 - v_y_13_21 <= 0.01
flow_n_y_13_21: - v_y_13_22 + v_y_13_21 <= 0.01
flow_p_x_13_23: v_x_13_22 - v_x_13_23 <= 0.01
flow_n_x_13_23: - v_x_13_22 + v_x_13_23 <= 0.01
flow_p_y_13_23: v_y_13_22 - v_y_13_23 <= 0.01
flow_n_y_13_23: - v_y_13_22 + v_y_13_23 <= 0.01
v_x_top_left_min_13_22: top_left_13_22 = 1 -> - v_x_13_22 <= 0.1
v_x_top_left_max_13_22: top_left_13_22 = 1 -> v_x_13_22 <= 0
v_y_top_left_min_13_22: top_left_13_22 = 1 -> - v_y_13_22 <= 0.1
v_y_top_left_max_13_22: top_left_13_22 = 1 -> v_y_13_22 <= 0
v_x_top_right_min_13_22: top_right_13_22 = 1 -> - v_x_13_22 <= 0
v_x_top_right_max_13_22: top_right_13_22 = 1 -> v_x_13_22 <= 0.1
v_y_top_right_min_13_22: top_right_13_22 = 1 -> - v_y_13_22 <= 0.1
v_y_top_right_max_13_22: top_right_13_22 = 1 -> v_y_13_22 <= 0
v_x_bottom_left_min_13_22: bottom_left_13_22 = 1 -> - v_x_13_22 <= 0.1
v_x_bottom_left_max_13_22: bottom_left_13_22 = 1 -> v_x_13_22 <= 0
v_y_bottom_left_min_13_22: bottom_left_13_22 = 1 -> - v_y_13_22 <= 0
v_y_bottom_left_max_13_22: bottom_left_13_22 = 1 -> v_y_13_22 <= 0.1
v_x_bottom_right_min_13_22: bottom_right_13_22 = 1 -> - v_x_13_22 <= 0
v_x_bottom_right_max_13_22: bottom_right_13_22 = 1 -> v_x_13_22 <= 0.1
v_y_bottom_right_min_13_22: bottom_right_13_22 = 1 -> - v_y_13_22 <= 0
v_y_bottom_right_max_13_22: bottom_right_13_22 = 1 -> v_y_13_22 <= 0.1
v_x_top_left_min_12_22: top_left_12_22 = 1 -> - v_x_12_22 <= 0.1
v_x_top_left_max_12_22: top_left_12_22 = 1 -> v_x_12_22 <= 0
v_y_top_left_min_12_22: top_left_12_22 = 1 -> - v_y_12_22 <= 0.1
v_y_top_left_max_12_22: top_left_12_22 = 1 -> v_y_12_22 <= 0
v_x_top_right_min_12_22: top_right_12_22 = 1 -> - v_x_12_22 <= 0
v_x_top_right_max_12_22: top_right_12_22 = 1 -> v_x_12_22 <= 0.1
v_y_top_right_min_12_22: top_right_12_22 = 1 -> - v_y_12_22 <= 0.1
v_y_top_right_max_12_22: top_right_12_22 = 1 -> v_y_12_22 <= 0
v_x_bottom_left_min_12_22: bottom_left_12_22 = 1 -> - v_x_12_22 <= 0.1
v_x_bottom_left_max_12_22: bottom_left_12_22 = 1 -> v_x_12_22 <= 0
v_y_bottom_left_min_12_22: bottom_left_12_22 = 1 -> - v_y_12_22 <= 0
v_y_bottom_left_max_12_22: bottom_left_12_22 = 1 -> v_y_12_22 <= 0.1
v_x_bottom_right_min_12_22: bottom_right_12_22 = 1 -> - v_x_12_22 <= 0
v_x_bottom_right_max_12_22: bottom_right_12_22 = 1 -> v_x_12_22 <= 0.1
v_y_bottom_right_min_12_22: bottom_right_12_22 = 1 -> - v_y_12_22 <= 0
v_y_bottom_right_max_12_22: bottom_right_12_22 = 1 -> v_y_12_22 <= 0.1
v_x_top_left_min_14_22: top_left_14_22 = 1 -> - v_x_14_22 <= 0.1
v_x_top_left_max_14_22: top_left_14_22 = 1 -> v_x_14_22 <= 0
v_y_top_left_min_14_22: top_left_14_22 = 1 -> - v_y_14_22 <= 0.1
v_y_top_left_max_14_22: top_left_14_22 = 1 -> v_y_14_22 <= 0
v_x_top_right_min_14_22: top_right_14_22 = 1 -> - v_x_14_22 <= 0
v_x_top_right_max_14_22: top_right_14_22 = 1 -> v_x_14_22 <= 0.1
v_y_top_right_min_14_22: top_right_14_22 = 1 -> - v_y_14_22 <= 0.1
v_y_top_right_max_14_22: top_right_14_22 = 1 -> v_y_14_22 <= 0
v_x_bottom_left_min_14_22: bottom_left_14_22 = 1 -> - v_x_14_22 <= 0.1
v_x_bottom_left_max_14_22: bottom_left_14_22 = 1 -> v_x_14_22 <= 0
v_y_bottom_left_min_14_22: bottom_left_14_22 = 1 -> - v_y_14_22 <= 0
v_y_bottom_left_max_14_22: bottom_left_14_22 = 1 -> v_y_14_22 <= 0.1
v_x_bottom_right_min_14_22: bottom_right_14_22 = 1 -> - v_x_14_22 <= 0
v_x_bottom_right_max_14_22: bottom_right_14_22 = 1 -> v_x_14_22 <= 0.1
v_y_bottom_right_min_14_22: bottom_right_14_22 = 1 -> - v_y_14_22 <= 0
v_y_bottom_right_max_14_22: bottom_right_14_22 = 1 -> v_y_14_22 <= 0.1
v_x_top_left_min_13_21: top_left_13_21 = 1 -> - v_x_13_21 <= 0.1
v_x_top_left_max_13_21: top_left_13_21 = 1 -> v_x_13_21 <= 0
v_y_top_left_min_13_21: top_left_13_21 = 1 -> - v_y_13_21 <= 0.1
v_y_top_left_max_13_21: top_left_13_21 = 1 -> v_y_13_21 <= 0
v_x_top_right_min_13_21: top_right_13_21 = 1 -> - v_x_13_21 <= 0
v_x_top_right_max_13_21: top_right_13_21 = 1 -> v_x_13_21 <= 0.1
v_y_top_right_min_13_21: top_right_13_21 = 1 -> - v_y_13_21 <= 0.1
v_y_top_right_max_13_21: top_right_13_21 = 1 -> v_y_13_21 <= 0
v_x_bottom_left_min_13_21: bottom_left_13_21 = 1 -> - v_x_13_21 <= 0.1
v_x_bottom_left_max_13_21: bottom_left_13_21 = 1 -> v_x_13_21 <= 0
v_y_bottom_left_min_13_21: bottom_left_13_21 = 1 -> - v_y_13_21 <= 0
v_y_bottom_left_max_13_21: bottom_left_13_21 = 1 -> v_y_13_21 <= 0.1
v_x_bottom_right_min_13_21: bottom_right_13_21 = 1 -> - v_x_13_21 <= 0
v_x_bottom_right_max_13_21: bottom_right_13_21 = 1 -> v_x_13_21 <= 0.1
v_y_bottom_right_min_13_21: bottom_right_13_21 = 1 -> - v_y_13_21 <= 0
v_y_bottom_right_max_13_21: bottom_right_13_21 = 1 -> v_y_13_21 <= 0.1
v_x_top_left_min_13_23: top_left_13_23 = 1 -> - v_x_13_23 <= 0.1
v_x_top_left_max_13_23: top_left_13_23 = 1 -> v_x_13_23 <= 0
v_y_top_left_min_13_23: top_left_13_23 = 1 -> - v_y_13_23 <= 0.1
v_y_top_left_max_13_23: top_left_13_23 = 1 -> v_y_13_23 <= 0
v_x_top_right_min_13_23: top_right_13_23 = 1 -> - v_x_13_23 <= 0
v_x_top_right_max_13_23: top_right_13_23 = 1 -> v_x_13_23 <= 0.1
v_y_top_right_min_13_23: top_right_13_23 = 1 -> - v_y_13_23 <= 0.1
v_y_top_right_max_13_23: top_right_13_23 = 1 -> v_y_13_23 <= 0
v_x_bottom_left_min_13_23: bottom_left_13_23 = 1 -> - v_x_13_23 <= 0.1
v_x_bottom_left_max_13_23: bottom_left_13_23 = 1 -> v_x_13_23 <= 0
v_y_bottom_left_min_13_23: bottom_left_13_23 = 1 -> - v_y_13_23 <= 0
v_y_bottom_left_max_13_23: bottom_left_13_23 = 1 -> v_y_13_23 <= 0.1
v_x_bottom_right_min_13_23: bottom_right_13_23 = 1 -> - v_x_13_23 <= 0
v_x_bottom_right_max_13_23: bottom_right_13_23 = 1 -> v_x_13_23 <= 0.1
v_y_bottom_right_min_13_23: bottom_right_13_23 = 1 -> - v_y_13_23 <= 0
v_y_bottom_right_max_13_23: bottom_right_13_23 = 1 -> v_y_13_23 <= 0.1
top_left_min_v_x_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 - 0.0729411765933037 abs_v_x_13_22 - pixel_13_22
<= -0.9960784316062927
top_left_max_v_x_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 + 0.0729411765933037 abs_v_x_13_22 - pixel_13_22
>= -0.9960784316062927
top_left_min_v_y_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 - 0.0729411765933037 abs_v_y_13_22 - pixel_13_22
<= -0.9960784316062927
top_left_max_v_y_13_22: top_left_13_22 = 1 -> 0.1176470518112183 v_x_13_22
- 0 v_y_13_22 + 0.0729411765933037 abs_v_y_13_22 - pixel_13_22
>= -0.9960784316062927
top_right_min_v_x_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.0545098036527634 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
top_right_max_v_x_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.0545098036527634 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
top_right_min_v_y_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.0545098036527634 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
top_right_max_v_y_13_22: top_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.0545098036527634 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_left_min_v_x_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
- 0.0117647051811218 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_left_max_v_x_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
+ 0.0117647051811218 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_left_min_v_y_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
- 0.0117647051811218 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_left_max_v_y_13_22: bottom_left_13_22 = 1 ->
0.1176470518112183 v_x_13_22 - 0 v_y_13_22
+ 0.0117647051811218 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_right_min_v_x_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.024705882370472 abs_v_x_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_right_max_v_x_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.024705882370472 abs_v_x_13_22 - pixel_13_22 >= -0.9960784316062927
bottom_right_min_v_y_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
- 0.024705882370472 abs_v_y_13_22 - pixel_13_22 <= -0.9960784316062927
bottom_right_max_v_y_13_22: bottom_right_13_22 = 1 ->
- 0.5450980365276337 v_x_13_22 - 0 v_y_13_22
+ 0.024705882370472 abs_v_y_13_22 - pixel_13_22 >= -0.9960784316062927
top_left_min_v_x_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 - 0.0607843138277531 abs_v_x_12_22
- pixel_12_22 <= -0.8784313797950745
top_left_max_v_x_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 + 0.0607843138277531 abs_v_x_12_22
- pixel_12_22 >= -0.8784313797950745
top_left_min_v_y_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 - 0.0607843138277531 abs_v_y_12_22
- pixel_12_22 <= -0.8784313797950745
top_left_max_v_y_12_22: top_left_12_22 = 1 -> 0.7568627521395683 v_x_12_22
+ 0.7294117659330368 v_y_12_22 + 0.0607843138277531 abs_v_y_12_22
- pixel_12_22 >= -0.8784313797950745
top_right_min_v_x_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
- 0.0729411765933037 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
top_right_max_v_x_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
+ 0.0729411765933037 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
top_right_min_v_y_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
- 0.0729411765933037 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
top_right_max_v_y_12_22: top_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.7294117659330368 v_y_12_22
+ 0.0729411765933037 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_left_min_v_x_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0282352976500988 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_left_max_v_x_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0282352976500988 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_left_min_v_y_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0282352976500988 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_left_max_v_y_12_22: bottom_left_12_22 = 1 ->
0.7568627521395683 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0282352976500988 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_right_min_v_x_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0117647051811218 abs_v_x_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_right_max_v_x_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0117647051811218 abs_v_x_12_22 - pixel_12_22 >= -0.8784313797950745
bottom_right_min_v_y_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
- 0.0117647051811218 abs_v_y_12_22 - pixel_12_22 <= -0.8784313797950745
bottom_right_max_v_y_12_22: bottom_right_12_22 = 1 ->
0.1176470518112183 v_x_12_22 + 0.1176470518112183 v_y_12_22
+ 0.0117647051811218 abs_v_y_12_22 - pixel_12_22 >= -0.8784313797950745
top_left_min_v_x_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.0545098036527634 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
top_left_max_v_x_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.0545098036527634 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
top_left_min_v_y_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.0545098036527634 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
top_left_max_v_y_14_22: top_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.0545098036527634 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
top_right_min_v_x_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.024705880926922 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
top_right_max_v_x_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.024705880926922 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
top_right_min_v_y_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
- 0.024705880926922 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
top_right_max_v_y_14_22: top_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.5450980365276337 v_y_14_22
+ 0.024705880926922 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_left_min_v_x_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.024705882370472 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_left_max_v_x_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.024705882370472 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_left_min_v_y_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.024705882370472 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_left_max_v_y_14_22: bottom_left_14_22 = 1 ->
- 0.5450980365276337 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.024705882370472 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_right_min_v_x_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.0243137254845351 abs_v_x_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_right_max_v_x_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.0243137254845351 abs_v_x_14_22 - pixel_14_22 >= -0.4509803950786591
bottom_right_min_v_y_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
- 0.0243137254845351 abs_v_y_14_22 - pixel_14_22 <= -0.4509803950786591
bottom_right_max_v_y_14_22: bottom_right_14_22 = 1 ->
- 0.4470588262192905 v_x_14_22 - 0.2470588237047195 v_y_14_22
+ 0.0243137254845351 abs_v_y_14_22 - pixel_14_22 >= -0.4509803950786591
top_left_min_v_x_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.00627450803294778 abs_v_x_13_21
- pixel_13_21 <= -0.9960784316062927
top_left_max_v_x_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.00627450803294778 abs_v_x_13_21
- pixel_13_21 >= -0.9960784316062927
top_left_min_v_y_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.00627450803294778 abs_v_y_13_21
- pixel_13_21 <= -0.9960784316062927
top_left_max_v_y_13_21: top_left_13_21 = 1 -> 0.8470588177442551 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.00627450803294778 abs_v_y_13_21
- pixel_13_21 >= -0.9960784316062927
top_right_min_v_x_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.0199999988079071 abs_v_x_13_21
- pixel_13_21 <= -0.9960784316062927
top_right_max_v_x_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.0199999988079071 abs_v_x_13_21
- pixel_13_21 >= -0.9960784316062927
top_right_min_v_y_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 - 0.0199999988079071 abs_v_y_13_21
- pixel_13_21 <= -0.9960784316062927
top_right_max_v_y_13_21: top_right_13_21 = 1 -> - 0 v_x_13_21
+ 0.199999988079071 v_y_13_21 + 0.0199999988079071 abs_v_y_13_21
- pixel_13_21 >= -0.9960784316062927
bottom_left_min_v_x_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
- 0.0729411765933037 abs_v_x_13_21 - pixel_13_21 <= -0.9960784316062927
bottom_left_max_v_x_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
+ 0.0729411765933037 abs_v_x_13_21 - pixel_13_21 >= -0.9960784316062927
bottom_left_min_v_y_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
- 0.0729411765933037 abs_v_y_13_21 - pixel_13_21 <= -0.9960784316062927
bottom_left_max_v_y_13_21: bottom_left_13_21 = 1 ->
0.8470588177442551 v_x_13_21 - 0 v_y_13_21
+ 0.0729411765933037 abs_v_y_13_21 - pixel_13_21 >= -0.9960784316062927
bottom_right_min_v_x_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 - 0.0545098036527634 abs_v_x_13_21 - pixel_13_21
<= -0.9960784316062927
bottom_right_max_v_x_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 + 0.0545098036527634 abs_v_x_13_21 - pixel_13_21
>= -0.9960784316062927
bottom_right_min_v_y_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 - 0.0545098036527634 abs_v_y_13_21 - pixel_13_21
<= -0.9960784316062927
bottom_right_max_v_y_13_21: bottom_right_13_21 = 1 -> - 0 v_x_13_21
- 0 v_y_13_21 + 0.0545098036527634 abs_v_y_13_21 - pixel_13_21
>= -0.9960784316062927
top_left_min_v_x_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
- 0.0117647051811218 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
top_left_max_v_x_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
+ 0.0117647051811218 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
top_left_min_v_y_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
- 0.0117647051811218 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
top_left_max_v_y_13_23: top_left_13_23 = 1 -> - 0 v_x_13_23 - 0 v_y_13_23
+ 0.0117647051811218 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
top_right_min_v_x_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
- 0.024705882370472 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
top_right_max_v_x_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
+ 0.024705882370472 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
top_right_min_v_y_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
- 0.024705882370472 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
top_right_max_v_y_13_23: top_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23
+ 0.024705882370472 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_left_min_v_x_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_x_13_23 - pixel_13_23 <= -0.9960784316062927
bottom_left_max_v_x_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_x_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_left_min_v_y_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_y_13_23 - pixel_13_23 <= -0.9960784316062927
bottom_left_max_v_y_13_23: bottom_left_13_23 = 1 -> - 0 v_x_13_23
- 0 v_y_13_23 - 0 abs_v_y_13_23 - pixel_13_23 >= -0.9960784316062927
bottom_right_min_v_x_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_x_13_23
- pixel_13_23 <= -0.9960784316062927
bottom_right_max_v_x_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_x_13_23
- pixel_13_23 >= -0.9960784316062927
bottom_right_min_v_y_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_y_13_23
- pixel_13_23 <= -0.9960784316062927
bottom_right_max_v_y_13_23: bottom_right_13_23 = 1 ->
- 0.7921568602323532 v_x_13_23 - 0 v_y_13_23 - 0 abs_v_y_13_23
- pixel_13_23 >= -0.9960784316062927
Bounds
pixel_13_22 <= 1
-0.1 <= v_x_13_22 <= 0.1
-0.1 <= v_y_13_22 <= 0.1
pixel_12_22 <= 1
-0.1 <= v_x_12_22 <= 0.1
-0.1 <= v_y_12_22 <= 0.1
pixel_14_22 <= 1
-0.1 <= v_x_14_22 <= 0.1
-0.1 <= v_y_14_22 <= 0.1
pixel_13_21 <= 1
-0.1 <= v_x_13_21 <= 0.1
-0.1 <= v_y_13_21 <= 0.1
pixel_13_23 <= 1
-0.1 <= v_x_13_23 <= 0.1
-0.1 <= v_y_13_23 <= 0.1
Binaries
top_left_13_22 top_right_13_22 bottom_left_13_22 bottom_right_13_22
top_left_12_22 top_right_12_22 bottom_left_12_22 bottom_right_12_22
top_left_14_22 top_right_14_22 bottom_left_14_22 bottom_right_14_22
top_left_13_21 top_right_13_21 bottom_left_13_21 bottom_right_13_21
top_left_13_23 top_right_13_23 bottom_left_13_23 bottom_right_13_23
General Constraints
abs_v_x_13_22: abs_v_x_13_22 = ABS ( v_x_13_22 )
abs_v_y_13_22: abs_v_y_13_22 = ABS ( v_y_13_22 )
abs_v_x_12_22: abs_v_x_12_22 = ABS ( v_x_12_22 )
abs_v_y_12_22: abs_v_y_12_22 = ABS ( v_y_12_22 )
abs_v_x_14_22: abs_v_x_14_22 = ABS ( v_x_14_22 )
abs_v_y_14_22: abs_v_y_14_22 = ABS ( v_y_14_22 )
abs_v_x_13_21: abs_v_x_13_21 = ABS ( v_x_13_21 )
abs_v_y_13_21: abs_v_y_13_21 = ABS ( v_y_13_21 )
abs_v_x_13_23: abs_v_x_13_23 = ABS ( v_x_13_23 )
abs_v_y_13_23: abs_v_y_13_23 = ABS ( v_y_13_23 )
End
-
Solving these two models on gurobi 8.11 and 9.0 beta,using Gurobi's default parameters, result in the same optimal solution of -6.090196028352e-02. The original model was found to have three solutions -0.060902 -0.0550549 -0.00117647, while the modified model resulted in only one solution -0.060902.
Are you using any parameters or stopping criteria?
0 -
No, but I'm using Gurobi 8.10. Do you think this could explain the difference?
0 -
I tested with 8.10, I see the same results as 8.1.1. Can you post your log files?
0 -
I upgraded to 8.1.1 and the error disappeared. Do you want me to roll back and post the log files? Otherwise the issue is resolved from my side.
0 -
I am glad the issues is gone. If you see it again, please resubmit a question with your log files.
0
Please sign in to leave a comment.
Comments
5 comments