How to solve a dual problem through Matlab

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

Answer 1

[Matt J]

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.