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Asked by Kai
on 12 Jan 2013

Hi, there,

How can I solve an optimization problem like following:

max_{\rho} min_{u} 1/2 * **u**^T * **K**(\rho) * **u** - **f**^T * **u**

the stiffness matrix K is related to the outer maximize problem design variable \rho. the inner minimize problem is the equilibrium with design variable **u** (displacements). The force vector **f** is given.

Thanks

Kai

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Answer by Matt J
on 12 Jan 2013

Edited by Matt J
on 12 Jan 2013

Accepted answer

The inner minimization can be solved analytically

u_min=K(rho)\f

and the problem reduces to

min_{rho} f^T * K(rho)\f

You could try using FMINUNC to solve it, although it's not clear how dense the local minima might be or how you would come up with a good initial guess. The Global Optimization Toolbox might be necessary.

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