Solving a constrained optimization problem

2015 4 23
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更新时间：2015 5 1
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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?

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Alan Weiss
Alan Weiss 2015-4-24

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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

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Erick
Erick 2015-4-30
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
Alan Weiss 2015-4-30
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
Erick 2015-5-1
That works. Thank you for your help!

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