Gurobi error 10020: Constraint Q not PSD (diagonal adjustment of 5.6e+01 would be required)
回答済み
Hi everyone.
I am solving an optimization with a quadratic constraint:
x'*Q*x + q'*x >= c.
Q is semi-definite positive. The adjustment requested is very large, so I assume is not an approximation error. What could be the cause? I also know that the constraint is not active for the optimum in the specific instance of the optimization I am performing (the objective function is limited by some other linear constraints).
Thanks!
If someone wants to have a look at the problem, this is as follows:
\ Model matlab
\ LP format - for model browsing. Use MPS format to capture full model detail.
Maximize
4.5 a_1_s_1 + 3.5 a_1_s_2 + 2.5 a_1_s_3 + 1.5 a_1_s_4 + 0.5 a_1_s_5
+ 4.5 a_2_s_1 + 3.5 a_2_s_2 + 2.5 a_2_s_3 + 1.5 a_2_s_4 + 0.5 a_2_s_5
Subject To
R0: a_1_s_1 <= 3
R1: a_1_s_2 <= 3
R2: a_1_s_3 <= 3
R3: a_1_s_4 <= 3
R4: a_1_s_5 <= 3
R5: a_2_s_1 <= 3
R6: a_2_s_2 <= 3
R7: a_2_s_3 <= 3
R8: a_2_s_4 <= 3
R9: a_2_s_5 <= 3
R10: a_1_s_1 <= 1.758458454848485
R11: a_1_s_1 + a_1_s_2 <= 1.758458454848485
R12: a_1_s_1 + a_1_s_2 + a_1_s_3 <= 1.758458454848485
R13: a_1_s_1 + a_1_s_2 + a_1_s_3 + a_1_s_4 <= 1.758458454848485
R14: a_1_s_1 + a_1_s_2 + a_1_s_3 + a_1_s_4 + a_1_s_5 <= 1.758458454848485
R15: a_2_s_1 <= 7.435834567878438
R16: a_2_s_1 + a_2_s_2 <= 7.435834567878438
R17: a_2_s_1 + a_2_s_2 + a_2_s_3 <= 7.435834567878438
R18: a_2_s_1 + a_2_s_2 + a_2_s_3 + a_2_s_4 <= 7.435834567878438
R19: a_2_s_1 + a_2_s_2 + a_2_s_3 + a_2_s_4 + a_2_s_5 <= 7.435834567878438
R20: a_1_s_1 >= -0.1
R21: a_1_s_2 >= -0.1
R22: a_1_s_3 >= -0.1
R23: a_1_s_4 >= -0.1
R24: a_1_s_5 >= -0.1
R25: a_2_s_1 >= -0.1
R26: a_2_s_2 >= -0.1
R27: a_2_s_3 >= -0.1
R28: a_2_s_4 >= -0.1
R29: a_2_s_5 >= -0.1
R30: a_1_s_1 >= -13.24154154515152
R31: a_1_s_1 + a_1_s_2 >= -13.24154154515152
R32: a_1_s_1 + a_1_s_2 + a_1_s_3 >= -13.24154154515152
R33: a_1_s_1 + a_1_s_2 + a_1_s_3 + a_1_s_4 >= -13.24154154515152
R34: a_1_s_1 + a_1_s_2 + a_1_s_3 + a_1_s_4 + a_1_s_5
>= -13.24154154515152
R35: a_2_s_1 >= -7.564165432121562
R36: a_2_s_1 + a_2_s_2 >= -7.564165432121562
R37: a_2_s_1 + a_2_s_2 + a_2_s_3 >= -7.564165432121562
R38: a_2_s_1 + a_2_s_2 + a_2_s_3 + a_2_s_4 >= -7.564165432121562
R39: a_2_s_1 + a_2_s_2 + a_2_s_3 + a_2_s_4 + a_2_s_5
>= -7.564165432121562
qc0: - 371.6306304681818 a_1_s_1 - 289.046045919697 a_1_s_2
- 206.4614613712121 a_1_s_3 - 123.8768768227273 a_1_s_4
- 41.29229227424243 a_1_s_5 - 582.11255555453 a_2_s_1
- 452.7542098757456 a_2_s_2 - 323.3958641969611 a_2_s_3
- 194.0375185181767 a_2_s_4 - 64.67917283939222 a_2_s_5 + [
20.25 a_1_s_1 ^2 + 31.5 a_1_s_1 * a_1_s_2 + 22.5 a_1_s_1 * a_1_s_3
+ 13.5 a_1_s_1 * a_1_s_4 + 4.5 a_1_s_1 * a_1_s_5 + 12.25 a_1_s_2 ^2
+ 17.5 a_1_s_2 * a_1_s_3 + 10.5 a_1_s_2 * a_1_s_4
+ 3.5 a_1_s_2 * a_1_s_5 + 6.25 a_1_s_3 ^2 + 7.5 a_1_s_3 * a_1_s_4
+ 2.5 a_1_s_3 * a_1_s_5 + 2.25 a_1_s_4 ^2 + 1.5 a_1_s_4 * a_1_s_5
+ 0.25 a_1_s_5 ^2 + 20.25 a_2_s_1 ^2 + 31.5 a_2_s_1 * a_2_s_2
+ 22.5 a_2_s_1 * a_2_s_3 + 13.5 a_2_s_1 * a_2_s_4
+ 4.5 a_2_s_1 * a_2_s_5 + 12.25 a_2_s_2 ^2 + 17.5 a_2_s_2 * a_2_s_3
+ 10.5 a_2_s_2 * a_2_s_4 + 3.5 a_2_s_2 * a_2_s_5 + 6.25 a_2_s_3 ^2
+ 7.5 a_2_s_3 * a_2_s_4 + 2.5 a_2_s_3 * a_2_s_5 + 2.25 a_2_s_4 ^2
+ 1.5 a_2_s_4 * a_2_s_5 + 0.25 a_2_s_5 ^2 ] >= -5554.576490445143
Bounds
End
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Hi Christian,
If \( Q \) is positive semidefinite, then the constraint \( x^\top Q x + c^\top x \leq b \) is convex, but the constraint \( x^\top Q x + c^\top x \geq b \) is not (in general). A simple example of this can be found in \( \mathbb{R}^2 \): the set \( \{ (x, y) : y^2 \leq x \} \) is convex, but the set \( \{ (x,y) : y^2 \geq x \} \) is not.
Nonetheless, Gurobi 9.0 is able to solve problems with non-convex constraints and objectives. To enable this, set the NonConvex parameter to 2.
I hope this helps. Thanks!
Eli
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