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Different optimization results between Yalmip and Mathematica

Answered
Jiayu Mi
  • Edited
Gurobi-versary
First Comment
First Question
The optimization model I want to o solve is shown as follows.
 
 
where uc0 and i are decision variables and Pbkmax, tbk, C, ucmax are all known.
Pbkmax=1497400;
tbk=13.9;
C=166/9*6;
ucmax=461.1.
 
I plot the image of S-uc0-I by Mathmetica, as shown below. It can be seen that S takes the maximum value when uc0=359.128 and i=811.86.
 
 
However, when I tried to solve this model by Gurobi/Yalmip, it prompted "Model is infeasible or unbounded".
I changed the lower limit of uc0 to 380,  the model can be solved. 
When I changed the upper limit of uc0 to 440,  the model can also be solved. 
 
 

clc
clear

Pbkmax=1497400;
tbk=13.9;
C=166/9*6;
ucmax=461.1;

uc0=sdpvar(1);
i=sdpvar(1);

x=sdpvar(1);
y=sdpvar(1);
z=sdpvar(1);
p=sdpvar(1);
q=sdpvar(1);

S=0.5*(-Pbkmax^2*C*tbk+C^2*Pbkmax*x+2*C*Pbkmax*tbk*q)*z+0.5*Pbkmax*tbk-0.5*C*x;

F=[];
F=F+[[0<=i<=(ucmax-uc0)*C/tbk]:'constraint1'];
e=10^(-5);
F=F+[[ucmax-Pbkmax*tbk/(4*C*ucmax)+e<=uc0<=ucmax]:'constraint2'];
% F=F+[[380<=uc0<=ucmax]:'constraint2']; %change lower limit of uc0
% F=F+[[ucmax-Pbkmax*tbk/(4*C*ucmax)+e<=uc0<=440]:'constraint2']; % change upper limit of uc0

F=F+[[x==uc0^2]:'constraint3'];
F=F+[[y==i^2]:'constraint4'];
F=F+[[p==x*y]:'constraint5'];
F=F+[[q==uc0*i]:'constraint6'];
F=F+[[z*(tbk*y+C*Pbkmax)==1]:'constraint7'];

options=sdpsettings('solver','gurobi');   
options.savesolveroutput=1;
output=optimize(F,-S,options);

Uc0=value(uc0)
I=value(i)
Ulin=ucmax-Pbkmax*tbk/(4*C*ucmax)
Ilin=(ucmax-Uc0)*C/tbk

 
From the figure above, we could see that S is smooth and bounded. So why  cannot  the model with 359.128<uc0<461.1  be solved?
 
Thank you. Look forward to your reply.
0

Comments

3 comments

Date Votes
  • Jaromił Najman
    Gurobi Staff Gurobi Staff
    • Edited

    Could you please share a model file? Please refer to How do I write an MPS model file from a third-party API? for all information about how to generate a model file out of Yalmip.

    Note that uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

    Best regards, 
    Jaromił

    0
  • Jiayu Mi
    Gurobi-versary
    First Comment
    First Question 
    NAME matlab
    ROWS
     N  OBJ
     L  R0      
     L  R1      
     L  R2      
     L  R3      
     E  qc0     
     E  qc1     
     E  qc2     
     E  qc3     
     E  qc4     
    COLUMNS
        C0        R1        7.9616306954436444e+00
        C0        R2        -1
        C0        R3        1
        C1        R0        -1
        C1        R1        1
        C2        OBJ       5.5333333333333329e+01
        C2        qc0       1
        C3        OBJ       0
        C3        qc1       1
        C4        OBJ       1.7245559593413333e+15
        C4        qc4       1.6571226666666666e+08
        C5        OBJ       0
        C5        qc2       1
        C6        OBJ       0
        C6        qc3       1
    RHS
        RHS1      OBJ       10406930
        RHS1      R1        3.6711079136690646e+03
        RHS1      R2        -3.5912806888485625e+02
        RHS1      R3        461.1
        RHS1      qc4       1
    BOUNDS
     FR BND1      C0      
     FR BND1      C1      
     FR BND1      C2      
     FR BND1      C3      
     FR BND1      C4      
     FR BND1      C5      
     FR BND1      C6      
    QUADOBJ
        C2        C4        -9.1694120888888874e+09
        C4        C6        -2.3034005066666665e+09
    QCMATRIX   qc0     
        C0        C0        -1
    QCMATRIX   qc1     
        C1        C1        -1
    QCMATRIX   qc2     
        C2        C3        -0.5
        C3        C2        -0.5
    QCMATRIX   qc3     
        C0        C1        -0.5
        C1        C0        -0.5
    QCMATRIX   qc4     
        C3        C4        6.95
        C4        C3        6.95
    ENDATA
    0
  • Jaromił Najman
    Gurobi Staff Gurobi Staff
    • Edited

    Thank you for sharing the model.

    The issue are the huge coefficients and infinite bounds for variables used in the optimization model. When you only plot a function, you just have to evaluate some function values to get a well scaled plot even for very big coefficients and variable values. This does not apply to optimization algorithms. Optimization algorithms are sensitive to bad scaling, i.e., huge/tiny coefficient values and unbounded variables in nonlinear terms.

    In order to properly solve your model, you have to re-scale it. In particular, you have to reduce the coefficient values and provide tight finite bounds for every variable participating in a bilinear term. Please refer to our Guidelines for Numerical Issues for more information.

    Best regards, 
    Jaromił

    0

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