Fmincon finds no solution with break Points

Hello, i want to solve the following Problem. I have the Problem that sometimes i get a solution to the Problem and sometimes not (for example if i set a breakpoint by cneq = f1(x)-z(1)-eps). If the Problem is not finding a solution then exitflag = -5 (does someone knows what -5 means?)

Does someone has an idea why sometimes i get a solution and sometimes not?

f1 =@(x) 10*(x(1)-2)^4+10*(x(1)-2)^3+10*(x(2)-2)^4+10*(x(2)-2)^3 + 10;
f2 =@(x) (x(1)-3)^2+(x(2)-3)^2 + 10;
Aneq = [-1 -1;
    1 0;
    0 1;
    -1 0;
    0 -1];
bneq = [-0.1; 10; 10; 0; 0];
x0 = [2.0595,2.0595];
z = [8.5913,14.6933];
eps = 1.4129;
[x,fval] = test(f1,f2,Aneq,bneq,x0,z,eps);

function [x,fval] = test(f1,f2,Aneq,bneq,x0,z,eps)
f = @(x) f2(x);
nonlincon = @constr;
    function [cneq,cq] = constr(x)
        cneq = f1(x)-z(1)-eps;
        cq = [];
    end
opts = optimoptions(@fmincon,'Algorithm','sqp', 'MaxFunctionEvaluations',3000,'FunctionTolerance', 1e-10,'ConstraintTolerance',1e-10);
problem = createOptimProblem('fmincon','objective',f,'x0',x0,'Aineq',Aneq,'bineq',bneq,'nonlcon',nonlincon,'options',opts);
gs = GlobalSearch;
gs.MaxTime = 1;
[x,fval,exitflag,output] = run(gs,problem);
if output.localSolverSuccess == 0
    return;
end
end

Thank you.

[Walter Roberson]

https://www.mathworks.com/help/gads/globalsearch.run.html#d123e65923

-5 is time limit exceeded.

Answer 1

[Torsten]

The code below works. Do you have an example where it fails ?

f1 =@(x) 10*(x(1)-2)^4+10*(x(1)-2)^3+10*(x(2)-2)^4+10*(x(2)-2)^3 + 10;
f2 =@(x) (x(1)-3)^2+(x(2)-3)^2 + 10;
lb = [0 0];
ub = [10 10];
Aneq = [-1 -1];
bneq = [-0.1];
x0 = [2.0595,2.0595];
z = [8.5913,14.6933];
eps = 1.4129;
[x,fval] = test(f1,f2,Aneq,bneq,lb,ub,x0,z,eps)

GlobalSearch stopped because it analyzed all the trial points.

All 13 local solver runs converged with a positive local solver exit flag.

x = 1×2

2.0583 2.0583

fval = 11.7735

exitflag = 1

output = struct with fields:
                funcCount: 2692
         localSolverTotal: 13
       localSolverSuccess: 13
    localSolverIncomplete: 0
    localSolverNoSolution: 0
                  message: 'GlobalSearch stopped because it analyzed all the trial points.↵↵All 13 local solver runs converged with a positive local solver exit flag.'

x = 1×2

2.0583 2.0583

fval = 11.7735

function [x,fval] = test(f1,f2,Aneq,bneq,lb,ub,x0,z,eps)
f = @(x) f2(x);
nonlincon = @constr;
    function [cneq,cq] = constr(x)
        cneq = f1(x)-z(1)-eps;
        cq = [];
    end
opts = optimoptions(@fmincon,'Algorithm','sqp', 'MaxFunctionEvaluations',3000,'FunctionTolerance', 1e-10,'ConstraintTolerance',1e-10);
problem = createOptimProblem('fmincon','objective',f,'x0',x0,'Aineq',Aneq,'bineq',bneq,'lb',lb,'ub',ub,'nonlcon',nonlincon,'options',opts);
gs = GlobalSearch;
gs.MaxTime = 1;
[x,fval,exitflag,output] = run(gs,problem)
if output.localSolverSuccess == 0
    return;
end
end

[Daniela Würmseer]

Yeah by me sometimes this example is working sometimes not. I get no solution for example if i put a breakpoint in line 6 (cneq = f1(x)-z(1)-eps;) from "test" and then continue the process of the function test by pressing "continue".

(The problem is that at this point of my algorithmus it is not finding a solution and the algorithm stops. And it should not do this. To exermine this problem a bit closer i build the function "test" to see where the Problem is. But when i run test i directly get a solution. (Except when i put breakpoints and run the function "test" step by step).

Do you know what exitflag -5 means?

[Torsten]

Walter answered this as "Time limit exceeded".

And better put bounds on the variables in lb and ub instead of Aineq and bineq.

[Daniela Würmseer]

Thank you I tried to put bounds in my Alg where i could have. But as my Algorithmus should work for different kind of Problems i cannot put bounds here.

I even already tried with gs.MaxTime = 10 but it changes nothing.