fmincon minimum number of iterations

Are there any way to set minimum number of iterations in fmincon.

I don't want to stop algorithm when

options.OptimalityTolerance = 0,

options.ConstraintTolerance = 0, and

options.StepTolerance = 0.

I want fmincon to stop at the desired iterations for comparing with other algorithms.

[Ameer Hamza]

So you want the algorithm to run even after it finds the optimal value?

[Shun Arahata]

Yes. I am solving a nonconvex optimization problem.

I think fmincon stops when first order KKT condition is satisfied.

So fmincon might stop at a saddle point (not global optima value ).

However, I am comparing with another algorithm which converge to second order stationary points (i.e. algorithm does not stop at a strict saddle point).

What I want to see is given fixed iteration numbers then fmincon stops at saddle point however another algortihm does not stop at saddle point.

A good example is as follows. from https://arxiv.org/abs/1907.04450

PGD( projected gradient descent) can't escape from saddle point.

So there is no change in loss value of PGD.

On the other hand, SNAP( proposed algorithm in the paper ) can escape from saddle point.

Answer 1

[Ameer Hamza]

This shows how you can force fmincon to keep searching until a fixed number of iterations is reached. It uses a simple objective function, but fmincon still run to 1000 iterations.

opts = optimoptions('fmincon', ...
    'OptimalityTolerance', 0, ...
    'StepTolerance', 0, ...
    'MaxFunctionEvaluations', inf,...
    'MaxIterations', 1000);

[X,f,~,out] = fmincon(@(x) x.^2, 1, [], [], [], [], [], [], [], opts);

[Shun Arahata]

This is exactly what I want to do. Thanks a lot.

[Ameer Hamza]

Glad to be of help.