ORTHOMADS: A DETERMINISTIC MADS INSTANCE WITH ORTHOGONAL DIRECTIONS

被引：167

作者：

Abramson, Mark A. ^{[1
]}

Audet, Charles ^{[2
,3
]}

Dennis, J. E., Jr. ^{[4
]}

Le Digabel, Sebastien ^{[2
,3
]}

机构：

[1] Boeing Co, Seattle, WA 98124 USA

[2] Ecole Polytech, Gerad, Montreal, PQ H3C 3A7, Canada

[3] Ecole Polytech, Dept Math & Genie Ind, Montreal, PQ H3C 3A7, Canada

[4] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA

来源：

SIAM JOURNAL ON OPTIMIZATION | 2009年 / 20卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

mesh adaptive direct search (MADS) algorithms; deterministic; orthogonal directions; constrained optimization; nonlinear programming; ADAPTIVE DIRECT SEARCH; OPTIMIZATION; DERIVATIVES; MINIMIZATION; ALGORITHMS; GRADIENTS;

D O I：

10.1137/080716980

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search (MADS) class of algorithms. The advantages of this new ORTHOMADS instantiation of MADS are that the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are orthogonal to each other, which yields convex cones of missed directions at each iteration that are minimal in a reasonable measure. Convergence results for ORTHOMADS follow directly from those already published for MADS, and they hold deterministically, rather than with probability one, as is the case for LTMADS, the first MADS instance. The initial numerical results are quite good for both smooth and nonsmooth and constrained and unconstrained problems considered here.

引用

页码：948 / 966

页数：19

共 28 条

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