Why are non-linear equality constraints not fulfilled for a constrained optimization problem using "fmincon" and "GlobalSearch"

I am trying to optimize 13 variables to maximize a cost function (depends on solutions of a dynamic system) . I have 2 linear equality constraints and 2 linear inequality constraints and 1 non-linear constraint. When I use "GlobalSearch" and "fmincon" as local solver, the linear equality constraints are fulfilled but non-linear equality constraint is not fulfilled. Also, if I use "fmincon" alone, the result shows no feasible solution found. 

 

I would like to know if I am putting the non-linear constraint correctly.

 

Answer 1

[MathWorks Support Team]

This behavior is expected, the solver might not be able to satisfy the non-linear constraints completely for all use cases. If the difference is a small value from the bound, the 'TolCon' property can be lowered by doing the following when creating the optimization options:

>> opts = optimoptions(@fmincon,'TolCon',1e-8);

Alternatively you can also try using the alternative algorithms such as ('sqp', 'active-set', 'interior-point') for "fmincon" to see if the constraints are satisfied. More details are available in the following link:

https://www.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-algorithms.html