MATLAB: What do the fields in the output structure of fmincon mean

convexfminconinterior-pointMATLABnonlinear optimizationOptimization Toolboxoutputquality

When we solve an optimization problem and obtain the output structure, it has fields such as funcCount, constrviolation, stepsize, firstorderopt etc.

According to the documentation, funcCount means function evaluations.

1. What is the difference between iterations and funcCount?

According to the documentation, constrviolations means maximum of constraint functions.

2. What does it mean to say maximum of constraint functions? In my problem, output.constrviolations = 0.1956. What does this mean?

3. How do I use these values to analyze quality of solution?

Iterations and Function Counts
Nonlinear constraint violations are the maximum of your nonlinear inequality constraint functions c(x), your nonlinear equality constraint functions |ceq(x)|, and your linear constraints A*x-b and |Aeq*x - beq|. The meaning of your positive value is that some of your constraints are not satisfied at the returned solution x.
That is up to you. You know that the constraints are not satisfied. Does that matter to you? If this problem is the same as that posted in another thread, then your output function stopped the optimization before fmincon reached what it considers to be a good solution.

Alan Weiss

MATLAB mathematical toolbox documentation

It's a case sensitivity issue. Instead of 'LB' and 'UB', pass in 'lb' and 'ub'.

Hi,

due to x² you have to use a nonlinear inequality. See details here:

In general you have to write a function like this:

function [c,ceq] = mycon(x)
    c = ...     % Compute nonlinear inequalities at x.
    ceq = ...   % Compute nonlinear equalities at x.
end

where c(x) is the array of nonlinear inequality constraints at x. fmincon attempts to satisfy:

c(x) <= 0

for all entries of c. ceq(x) is the array of nonlinear equality constraints at x. fmincon attempts to satisfy:

ceq(x) = 0

for all entries of ceq.

So it is needed to rewrite your condition i a way, that this condition is fulfilled. A good resource with example you find here:

Best regards

Stephan