which solver I can use to solve a non linear problem with 36000 variables and 24000 constraints?

I should solve a problem with multiple variables ( about 36000, due to the use of 4 different indices) and 24000 constraints (equalities and inequalities,only few are non-linear constraints).I adopted fmincon solver but it goes to overflow. Is there any fitting solver for my problem?

Answer 1

[Matt J]

If you have nonlinear constraints, then fmincon is what you should use. To deal with the large size of the problem, you should be using sparse matrices for your linear equality and inequality constraints. You should also use GradObj and GradConstr options to provide your own analytical gradient calculations. Same thing with any Hessian calculations that the algorithm requires. The default finite difference derivative calculations will be very time consuming in light of the number of variables that you have.

[GAETANO CIANCITTO]

thanks for your answer. What about using simulated annealing solver? if it's efficient for my problem, Can I associate a multidimensional array to it?

[Matt J]

You could try. However, if your function is continuous/differentiable, it would make more sense to use a solver like fmincon which can take advantage of that.

I don't see what relevance the multidimensionality of the array would have with any MATLAB solver. You can always do X=X(:).

[GAETANO CIANCITTO]

fmincon requires undefined time; 1-can Ga solver fit better? 2-is Ga solver in the optimtool enough or Do I need an external solver (Ga toolbox )? thank you in advance

[Matt J]

ga is in the Global Optimization Toolbox. All algorithms require undefined time, but all have options to let you cap the number of iterations or control other stopping criteria.