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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 180; no. 2; pp. 391 - 412
Main Authors: Jian, Jin-Bao, Tang, Chun-Ming, Hu, Qing-Jie, Zheng, Hai-Yan
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.08.2005
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2004.11.008