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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 7, Pages 1184–1196
(Mi zvmmf4717)
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This article is cited in 22 scientific papers (total in 22 papers)
Optimality conditions and newton-type methods for mathematical programs with vanishing constraints
A. F. Izmailov, A. L. Pogosyan Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Abstract:
A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanical structures can be reduced to problems of this kind. Problems in this class are difficult to analyze and solve numerically because their constraints are usually irregular. Some known first- and second-order necessary conditions for local optimality are refined for problems with vanishing constraints, and special Newton-type methods are developed for solving such problems.
Key words:
mathematical program with vanishing constraints, mathematical program with complementarity constraints, constraint qualification, optimality conditions, sequential quadratic programming, active-set method.
Received: 14.11.2008
Citation:
A. F. Izmailov, A. L. Pogosyan, “Optimality conditions and newton-type methods for mathematical programs with vanishing constraints”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1184–1196; Comput. Math. Math. Phys., 49:7 (2009), 1128–1140
Linking options:
https://www.mathnet.ru/eng/zvmmf4717 https://www.mathnet.ru/eng/zvmmf/v49/i7/p1184
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Abstract page: | 358 | Full-text PDF : | 123 | References: | 40 | First page: | 8 |
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