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Mesh adaptive direct search algorithms for constrained optimization. (English) Zbl 1112.90078

Summary: This paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available. We introduce the mesh adaptive direct search (MADS) class of algorithms which extends the generalized pattern search (GPS) class by allowing local exploration, called polling, in an asymptotically dense set of directions in the space of optimization variables. This means that under certain hypotheses, including a weak constraint qualification due to Rockafellar, MADS can treat constraints by the extreme barrier approach of setting the objective to infinity for infeasible points and treating the problem as unconstrained.

MSC:

90C30 Nonlinear programming
90C56 Derivative-free methods and methods using generalized derivatives
65K05 Numerical mathematical programming methods
49J52 Nonsmooth analysis
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