A feasible descent SQP algorithm for general constrained optimization without strict complementarity

In this paper, a class of optimization problems with equality and inequality constraints is discussed. Firstly, the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter. The later problem is shown to be equivalent to the original problem i...

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Vydané v:	Journal of computational and applied mathematics Ročník 180; číslo 2; s. 391 - 412
Hlavní autori:	Jian, Jin-Bao, Tang, Chun-Ming, Hu, Qing-Jie, Zheng, Hai-Yan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 15.08.2005 Elsevier
Predmet:	Calculus of variations and optimal control Exact sciences and technology Feasible descent algorithm General constrained optimization Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use SQP Strict complementarity Superlinear convergence General constrained optimization 49M30 90C30 SQP Superlinear convergence Feasible descent algorithm Strict complementarity Optimization method 49M30 General constrained optimization Numerical method Convergence Constrained optimization Numerical analysis Applied mathematics Inequality constraint Equality constraint Mathematical programming
ISSN:	0377-0427, 1879-1778
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Abstract	In this paper, a class of optimization problems with equality and inequality constraints is discussed. Firstly, the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter. The later problem is shown to be equivalent to the original problem if the parameter is large enough (but finite), then a feasible descent SQP algorithm for the simplified problem is presented. At each iteration of the proposed algorithm, a master direction is obtained by solving a quadratic program (which always has a feasible solution). With two corrections on the master direction by two simple explicit formulas, the algorithm generates a feasible descent direction for the simplified problem and a height-order correction direction which can avoid the Maratos effect without the strict complementarity, then performs a curve search to obtain the next iteration point. Thanks to the new height-order correction technique, under mild conditions without the strict complementarity, the globally and superlinearly convergent properties are obtained. Finally, an efficient implementation of the numerical experiments is reported.
AbstractList	In this paper, a class of optimization problems with equality and inequality constraints is discussed. Firstly, the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter. The later problem is shown to be equivalent to the original problem if the parameter is large enough (but finite), then a feasible descent SQP algorithm for the simplified problem is presented. At each iteration of the proposed algorithm, a master direction is obtained by solving a quadratic program (which always has a feasible solution). With two corrections on the master direction by two simple explicit formulas, the algorithm generates a feasible descent direction for the simplified problem and a height-order correction direction which can avoid the Maratos effect without the strict complementarity, then performs a curve search to obtain the next iteration point. Thanks to the new height-order correction technique, under mild conditions without the strict complementarity, the globally and superlinearly convergent properties are obtained. Finally, an efficient implementation of the numerical experiments is reported.
Author	Tang, Chun-Ming Zheng, Hai-Yan Jian, Jin-Bao Hu, Qing-Jie
Author_xml	– sequence: 1 givenname: Jin-Bao surname: Jian fullname: Jian, Jin-Bao email: jianjb@gxu.edu.cn – sequence: 2 givenname: Chun-Ming surname: Tang fullname: Tang, Chun-Ming – sequence: 3 givenname: Qing-Jie surname: Hu fullname: Hu, Qing-Jie – sequence: 4 givenname: Hai-Yan surname: Zheng fullname: Zheng, Hai-Yan
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Cites_doi	10.1137/0728063 10.1137/0729072 10.1007/978-3-642-48320-2 10.1137/S1064827598334861 10.1007/BFb0120947 10.1137/0325051 10.1023/A:1022655423083 10.1007/BF01580371 10.1007/BF01581247 10.1007/BFb0067703 10.1080/10556789608805638 10.1007/BF00941288 10.1137/S1052623497326629 10.1007/BF00932858 10.1137/S1052623498344562 10.1007/s11766-000-0057-9 10.1007/BF01582123 10.1007/BF02591987 10.1007/BFb0120945 10.1137/0326046 10.1007/BF00940684 10.1017/S0962492900002518
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Keywords	General constrained optimization 49M30 90C30 SQP Superlinear convergence Feasible descent algorithm Strict complementarity Optimization method 49M30 General constrained optimization Numerical method Convergence Constrained optimization Numerical analysis Applied mathematics Inequality constraint Equality constraint Mathematical programming
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Snippet	In this paper, a class of optimization problems with equality and inequality constraints is discussed. Firstly, the original problem is transformed to an...
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SubjectTerms	Calculus of variations and optimal control Exact sciences and technology Feasible descent algorithm General constrained optimization Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use SQP Strict complementarity Superlinear convergence
Title	A feasible descent SQP algorithm for general constrained optimization without strict complementarity
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