maximizing the norm of a matrix using fmincon

Hello! I am trying to find the maximum of |A(z)|_2. A(z) is a n x n real matrix. Each entry in this matrix consists of some nonlinear equation. For context, A is the jacobian of a nonlinear dynamical system and I need to find the upper bound on the norm of this jacobian. the decision vector z (n x 1) is upper and lower bounded. My code works but I get a value of the norm which is extremely large, perhaps I have a bug in the code. Here it is (with some simpliciations):

A = @(z) [....];
lb = [...];
ub = [...];
z0 = [...];

fun = @(z) -norm(A(z),2);
options = optimoptions('fmincon');
options.Algorithm = 'interior-point';
zStar = fmincon(fun,z0,[],[],[],[],lb,ub,[],options);

disp(norm(A(zStar),2));

Is there anything wrong with this code? I am not sure I have defined the objective function correctly, I have not found any examples of this.

Best Regards MC

Answer 1

[Alan Weiss]

What makes you think that there is anything wrong? You get a very large answer. Great! fmincon was trying to maximize. Is the answer feasible, meaning does the answer satisfy the bounds? If so, then I don't see a problem.

Alan Weiss

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