how to use fmincon to optimize a functio with more than one control vector where the control vectors used in constrains also?

I have three unknown vectors, matrices p, X, L with which I have to optimize a function norm(sp) [s is known] and these vectors are used in constraints also,

I cannot figured it out how to write p X L in one vector as in fmincon only one input vector is allowed.

Thank you so much for your help

Answer 1

[Matt J]

Use the problem-based optimization framework to launch fmincon. It will look approximately like,

p=optimvar('p',pi,pj);
X=optimvar('X',Xi,Xj);
L=optimvar('L',Li,Lj);

objfun=fcn2optimexpr(@(pp) norm(s*pp)  , p);
nlcon=fcn2optimexpr(@(pp,XX,LL) nlconFcn(pp,XX,LL)  , p, X, L);

prob = optimproblem('Objective',objfun,'Constraints',nlcon)

Initial.p=__
Initial.X=__
Initial.L=___
Final=solve(prob,Initial,'Solver','fmincon')

[Parna]

Thankyou so much. This framework helped me for this doubt.

Answer 2

[Torsten]

If all three vectors/matrices are to be treated as solution variables for "fmincon", use

v = [p(:);X(:);L(:)]

It's useful to transfer the sizes of the three components of the vector v to the functions used by "fmincon" in order to recover p, X and L from v.

[Parna]

I tried this method previously but this method is very confusing in case of orders of the matrices. problem based Optimization Framework worked for me.

Thank you.