Audet, Charles; Dennis, J. E. jun. Mesh adaptive direct search algorithms for constrained optimization. (English) Zbl 1112.90078 SIAM J. Optim. 17, No. 1, 188-217 (2006). 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. Cited in 3 ReviewsCited in 239 Documents MSC: 90C30 Nonlinear programming 90C56 Derivative-free methods and methods using generalized derivatives 65K05 Numerical mathematical programming methods 49J52 Nonsmooth analysis Keywords:mesh adaptive direct search algorithms (MADS); convergence analysis; constrained optimization; nonsmooth analysis; Clarke derivatives; hypertangent; contingent cone PDFBibTeX XMLCite \textit{C. Audet} and \textit{J. E. Dennis jun.}, SIAM J. Optim. 17, No. 1, 188--217 (2006; Zbl 1112.90078) Full Text: DOI Link