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MiniMax Problems (MMP)
 \mathbf{max_{k=0,...,K}\{f_k(x)\} \to min}
subjected to
\mathbf{lb} \le \mathbf{x} \le \mathbf{ub}
\mathbf{A x} \le \mathbf{b}
\mathbf{A}_\mathbf{eq} \mathbf{x} = \mathbf{b}_\mathbf{eq}
 \mathbf{\forall i=0,...,I: c_i(x) \le 0}
 \mathbf{\forall j=0,...,J: h_j(x) = 0}
 \mathbf{ \{ {f, c_i, h_j :R^n \to R \} \subset C^1}}
(smooth differentiable functions)
\mathbf{x \in R^n}

OpenOpt MMP example >>>

MMP solvers connected to OpenOpt:

Solver License Info
converter to NLP example: r = p.solve('nlp:ipopt') (see the example). See NLP for list of the NLP solvers available.
nsmm BSD This one is quite primitive. Can handle linear & non-lin constraints, user-supplied gradients/subgradients df, dc, dh. The solver is intended to be enhanced in future. It just tries to solve NSP max(f_k(x)) \to min

For FuncDesigner problems you could consider using interalg - it can handle min and max functions.

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