How can I change step tolerance, optimality measure, or optimaility/consraint tolerance for a non-linear optimization problem?

I am trying to maximize a non-linear optimization problem using the Optimization Toolbox. However, I run into an issue when I attempt to solve, as it finds essentially whatever initial point I give (that is inside the constraint range) to be a local minimum and it does not attempt to maximize the objective. I get the following message:

Initial point is a local minimum that satisfies the constraints.

Optimization completed because at the initial point, the objective function is non-decreasing

in feasible directions to within the value of the optimality tolerance, and

constraints are satisfied to within the value of the constraint tolerance.

...

Optimization completed: The final point is the initial point.

The first-order optimality measure, 0.000000e+00, is less than options.OptimalityTolerance =

1.000000e-06, and the maximum constraint violation, 0.000000e+00, is less than

options.ConstraintTolerance = 1.000000e-06.

I've looked online about trying to change these various characteristics, but I've only found solutions changing it for when one directly runs a command like fmincon; I'm not sure how it needs to be changed for my setup here. I have the (relevant) code below, I can provide more if needed. Thank you.

pllPM = optimproblem('ObjectiveSense','maximize');
...
c1_pico = optimvar('cap1', 1);
...
con_min = c1_pico >= 1E-1;
con_max = c1_pico <= 1E1;

pllPM.Constraints.cap_max = con_max;
pllPM.Constraints.cap_min = con_min;
...
pllPM.Objective = atan(r1*c1*unity) - atan(r1*c_eq*unity);
show(pllPM)
c0.cap1 = 5;
c1_struct = solve(pllPM, c0)

[Matt J]

It appears that you have only a single unknown variable. It may therefore be better just to use fminsearch or fminbnd.

Answer 1

[Matt J]

This example shows how you can pass an optimoptions object to the solver

https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationproblem.solve.html#mw_885c21ff-3ac9-44f7-bd47-80fbfb6dceaa

However, one reason why it may not be progressing past the initial point is if you are initializing in a region with very low gradient. Note that if r1*c1*unity and r1*c_eq*unity are large, the atan() terms will have very smalll slope.