A new feasible descent algorithm combining SQP with generalized projection for optimization problems without strict complementarity

In this paper, optimization problems with nonlinear inequality constraints are discussed, by combining the sequential quadratic programming (SQP) with an new generalized projection technique, a new feasible descent algorithm for solving the problems is presented. At each iteration of the new algorit...

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Veröffentlicht in:Applied mathematics and computation Jg. 162; H. 3; S. 1065 - 1081
1. Verfasser: Jian, Jin-Bao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Elsevier Inc 25.03.2005
Elsevier
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Calculus of variations and optimal control
Computer science; control theory; systems
Constrained optimization
Exact sciences and technology
Feasible descent algorithm
Generalized projection
Mathematical analysis
Mathematics
Nonlinear inequality
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
SQP
Superlinear convergence
Theoretical computing
Superlinear convergence
SQP
Feasible descent algorithm
Generalized projection
Nonlinear inequality
Constrained optimization
Numerical analysis
Applied mathematics
Sequential method
Inequality constraint
Optimization method
Convergence rate
Complementarity problem
Nonlinear problems
Objective function
Quadratic programming
Mathematical programming
ISSN:0096-3003, 1873-5649
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Beschreibung
Zusammenfassung:In this paper, optimization problems with nonlinear inequality constraints are discussed, by combining the sequential quadratic programming (SQP) with an new generalized projection technique, a new feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) is solved and a master direction is obtained, and an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction, both this two correction formulas contain a new generalized projection technique. Under weaker conditions without the strict complementarity, the new algorithm is proved to possess global convergence and superlinear convergence. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.01.016