Convergence of Mesh Adaptive Direct Search to Second‐Order Stationary Points | Zendy

Mark A. Abramson | Zendy; Charles Audet | Zendy

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Convergence of Mesh Adaptive Direct Search to Second‐Order Stationary Points

Author(s) -

Mark A. Abramson,

Charles Audet

Publication year - 2006

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/050638382

Subject(s) - mathematics , subsequence , mathematical optimization , iterated function , convergence (economics) , stationary point , set (abstract data type) , minification , class (philosophy) , computer science , artificial intelligence , mathematical analysis , economics , bounded function , programming language , economic growth

A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search (MADS) algorithms for general constrained optimization. Because of the ability of MADS to generate an asymptotically dense set of search directions, we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems.

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