Solving a constrained optimization problem

I am trying to solve an optimization problem in matlab:

minimize( sum_{i,j}(f(M(i,j))) + err )

subject to: - norm(M) < err

- err > 0

- if j == i+1: M(i,j) > 1

- if j == i-1: M(i,j) < -1

- else: -1 <= M(i,j) <= 1

where: - f is a non convex function in general

- M is an n by n matrix

I looked at the constrained optimization toolbox but could not find how to solve this problem.

Can anyone point me which function I should use?

Answer 1

[Alan Weiss]

If you look in the Optimization Decision Table you see that for a constrained nonlinear problem you should use fmincon. The constraint norm(M) < err is a nonlinear inequality constraint. The other constraints on M(i,j) are bound constraints.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Erick]

Thank you. so, to make sure, since I want to optimize overM and err, I need to create a vector A = [M(:),err], extract M and reshape it inside the objective function?

[Alan Weiss]

That sounds right, with the proviso that you make

 A = [M(:);err];

I mean, make a column vector, using a semicolon before err.

Alan Weiss

MATLAB mathematical toolbox documentation

[Erick]

That works. Thank you for your help!