Constraint tolerance setting is not working

I'm using fmincon for optimizing a system for trajectory optimization. Recently, my optimization problem seems to go well below 1e-06 feasibility for the 'interior point' solver. For this project, I will have to perform multiple trajectory optimizations and hence want my sovler to stop < 1e-06 feasibility. When I add the option of constraint tolerance, the solver continues to further iterate. How do I tackle this problem. I found the same problem wiith StepTolerance option as well

Answer 1

[Matt J]

You need to demonstrate the problem with code, but based on your description, nothing is obviously wrong as far as the constraint tolerance is concerned. Even though you may see the constraint tolerance met, it doesn't mean an optimal point has been found yet. Imagine if you had no constraints. Then the constraint tolerance would be satisfied vacuously at every iteration, but of course it would be wrong for the solver not to iterate...

I found the same problem wiith StepTolerance option as well

That, you would need to demonstrate for us.

[mekg_10]

Thanks for the reply Matt. I do understand that just because my constraint tolerance is met, doesn't mean I have an optimal solution. I just don't want my solver to continue to solving till my max iterations but rather stop when the my constraints tolerance is met. In my question, I've mentioned I only need a <1e-06 feasibility, I don't need my solver to keep solving till the optimal point. Is there any way to stop the optimization if the feasibility reaches this bound. Hope I've made my question clear

[Matt J]

Yes, you can just set the objective function to a constant, e.g.,

f=@(x) 0

Then, all points will be optimal and the only criterion fmincon will use for stopping is satisfaction of the constraints.

[Matt J]

Alternatively, you can implement your own stopping criterion via the OutputFcn option,

https://www.mathworks.com/help/optim/ug/output-function.html

Answer 2

[Catalytic]

It is a classic mistake to define the stopping tolerances with optimoptions, but forget to pass them to fmincon, as in -

options=optimoptions('fmincon','StepTolerance',1e-6,'ConstraintTolerance',1e-6);

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon) %Forgot to give options to fmincon

I wonder if that may be why you aren't seeing your settings obeyed.

[Matt J]

If that was the reason, it's a case in point for why you always have to demonstrate your issue with code...

[mekg_10]

options = optimoptions('fmincon', 'Display','iter', 'MaxFunctionEvaluations', 1e6, 'MaxIterations', 1000, 'ConstraintTolerance', 1e-03);

lb = [-1500*ones(n,1); -1500*ones(n,1); 0*ones(n,1); -10*ones(n,1); 0*ones(n,1); -100*ones(n,1);
    -0.5*pi*ones(n,1); -0.5*pi*ones(n,1); -0.5*pi*ones(n,1); -0.5*pi*ones(n,1); -0.5*pi*ones(n,1); -0.5*pi*ones(n,1); -50000*ones(n,1);
    -50000*ones(n,1); -50000*ones(n,1); 0];   %lower bound of states, control variables and time

ub = [1000*ones(n,1); 1500*ones(n,1); 2000*ones(n,1); 0*ones(n,1); 0*ones(n,1); 100*ones(n,1);
    0.5*pi*ones(n,1); 0.5*pi*ones(n,1); 0.5*pi*ones(n,1); 0.5*pi*ones(n,1); 0.5*pi*ones(n,1); 0.5*pi*ones(n,1); 50000*ones(n,1);
    50000*ones(n,1); 50000*ones(n,1); 2000]; %upper bound of states, control variables and time

[x, fval] = fmincon(@(x) objective(x, n, D), x0, [], [], [], [], lb, ub, @(x) constraints(x, D, n, BCs), options);

@Catalytic @Matt JThis is my code snippet defining the options and calling the fmincon function. I wish forgetting to add the options was my mistake xD. Maybe I'm doing something else wrong here, please point out if so

[Matt J]

That looks alright, to me at least. But as I said in my answer, if you have such little interest in achieving the optimum of the objective, you may as well just set it to a constant.

Aside from that, a few miscellaneous remarks:

(1) It would be more readable and efficeint to use repelem instead of repeated calls to ones(n,1).

lb = [-1500; 0; -10; 0; -100; -0.5*pi; -0.5*pi; -0.5*pi; -0.5*pi; -0.5*pi; -0.5*pi; -50000;
    -50000; -50000];   %lower bound of states, control variables and time
lb=[repelem(lb,n);0];

ub = [1000; 1500; 2000; 0; 0; 100;
    0.5*pi; 0.5*pi; 0.5*pi; 0.5*pi; 0.5*pi; 0.5*pi; 50000;
    50000; 50000]; %upper bound of states, control variables and time
ub=[repelem(ub,n);2000];

(2) Your unknown variables seem to have very different scales. It can sometimes help performance to change units to make them more comparable in scale, for example, by expressing any angles in degrees instead of radians.