A new exact penalty method for semi-infinite programming problems

In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty...

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Vydané v:Journal of computational and applied mathematics Ročník 261; s. 271 - 286
Hlavní autori: Lin, Qun, Loxton, Ryan, Teo, Kok Lay, Wu, Yong Hong, Yu, Changjun
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.05.2014
Predmet:
Constrained optimization
Exact penalty function
Nonlinear programming
Semi-infinite programming
Semi-infinite programming
Nonlinear programming
Exact penalty function
Constrained optimization
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact—that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.11.010