Penlab problem: PenLab didn't converge: unconstrained minimization failed

optimizer

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Jan 17, 2020, 8:59:10 AM1/17/20

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Dear Prof.Lofberg,

I am solving a problem with a BMI constraint as follows:

(A1 is a numerical matrix 10x10 dimension dynamic state space matrix, while Bss is the input state space matrix with dimension 10x1).

X=sdpvar(10,10),'symmetric');

kr=sdpvar(6,1);

ind1=0.99995;

ind2=0.01;

BMI_11=ind1*(A1*X-Bss*kr'*V'*X+X*A1'-X*V*kr*Bss');

BMI_12=ind2*(A1*X-Bss*kr'*V'*X-X*A1'+X*V*kr*Bss');

BMI_21=ind2*(-A1*X+Bss*kr'*V'*X+X*A1'-X*V*kr*Bss');

BMI_22=ind1*(A1*X-Bss*kr'*V'*X+X*A1'-X*V*kr*Bss');

BMI=[BMI_11 BMI_12; BMI_21 BMI_22];

epsilon_A=1e-4;

epsilon_B=1e-4;

epsilon_costfun=1e-4;

ConstrBMI=[BMI<=-epsilon_A*eye(size(BMI,1))]+[X>=epsilon_B*eye(size(X,1))];

opts=sdpsettings('solver','penlab');

diagnostics = optimize(ConstrBMI,epsilon_costfun*norm(V*kr)^2,opts);

[Rdamp,pdamp]=chol(-value(BMI_damp));

*******************************************************************************

PenLab 1.04 (20140125)

*******************************************************************************

Number of variables 61

Number of matrix variables 0

- degrees of freedom (var. elements) 0

(Function) constraints

- box inequalities 0

- linear inequalities 0

- nonlinear inequalities 0

- linear equalities 0

- nonlinear equalities 0

Matrix constraints

- box inequalities 0

- linear inequalities 1

- nonlinear inequalities 1

*******************************************************************************

* it | obj | (U,G(x)) | ||dF|| | feas | pmin | Nwt | InIt |

*******************************************************************************

| 0| 0.00000e+00 | 0.0e+00 | 9.2e+05 | 1.0e-04 | 6.9e-01 | 0 | 0 |

| 1| 2.07386e-01 | 0.0e+00 | 3.8e-05 | 1.3e-01 | 6.9e-01 | 90 | 160 |

| 2| 1.98025e-01 | 0.0e+00 | 6.9e-03 | 1.2e-02 | 3.5e-01 | 40 | 91 |

| 3| 1.96981e-01 | 0.0e+00 | 8.5e-04 | 1.2e-03 | 1.7e-01 | 34 | 103 |

| 4| 1.96831e-01 | 0.0e+00 | 4.2e-03 | 4.6e-04 | 8.7e-02 | 20 | 66 |

| 5| 1.96800e-01 | 0.0e+00 | 5.5e-03 | 2.3e-04 | 4.3e-02 | 30 | 90 |

| 6| 1.96797e-01 | 0.0e+00 | 9.2e-03 | 1.6e-04 | 2.2e-02 | 69 | 209 |

| 7| 1.96796e-01 | 0.0e+00 | 4.3e-01 | 1.4e-04 | 1.1e-02 | 100 | 294!|

| 8| 1.96796e-01 | 0.0e+00 | 4.6e-01 | 1.5e-04 | 5.4e-03 | 100 | 308!|

| 9| 1.96796e-01 | 0.0e+00 | 2.0e-01 | 1.5e-04 | 2.7e-03 | 100 | 300!|

*******************************************************************************

PenLab didn't converge: unconstrained minimization failed

*******************************************************************************

Objective 1.9679597668732166E-01

Relative precision 1.2849995468558473E-03

Compl. Slackness 0.0000000000000000E+00

Grad augm. lagr. 2.0192984135115874E-01

Feasibility (max) 0.0000000000000000E+00

Newton steps 583

Inner steps 1621

Linesearch steps 1089

Number of evaluations of

- function values 1130

- gradient values 592

- hessian values 583

Time statistics

- total process time 58.6094 s

- all minimization steps 58.3125 s

- all factorizations 0.84375 s

- function values evaluation 3.57813 s

- gradient values evaluation 7.92188 s

- hessian values evaluation 45.375 s

*******************************************************************************

What do you suggest to solve the problem?

Johan Löfberg

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Jan 17, 2020, 9:01:22 AM1/17/20

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I've never had any good results with penlab, and cannot give any advice.

optimizer

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Jan 17, 2020, 9:23:13 AM1/17/20

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Which solver do you suggest for my problem?

Johan Löfberg

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Jan 17, 2020, 9:37:05 AM1/17/20

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There are no (sufficiently well) working solvers for nonlinear SDPs

Most often you are best off to develop some heuristic based on linearizations, line-search, trust-region, alternating directions etc etc with problems solved along the way using a good sdp solver such as mosek

Best though is to spend effort on developing linear models.

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