A Sequential Quadratic Programming Method Without A Penalty Function or a Filter for Nonlinear Equality Constrained Optimization

We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected...

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Veröffentlicht in:SIAM journal on optimization Jg. 21; H. 2; S. 545 - 571
Hauptverfasser: Liu, Xinwei, Yuan, Yaxiang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.04.2011
Schlagworte:
Algorithms
Applied mathematics
Computational mathematics
Mathematical functions
Methods
Optimization
Quadratic programming
Violations
ISSN:1052-6234, 1095-7189
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Abstract We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush-Kuhn-Tucker point, an approximate Fritz-John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the [cursive l]2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without requiring linear independence constraint qualification, the algorithm is shown to be locally superlinearly convergent. The preliminary numerical results show that the algorithm is robust and efficient when solving some small- and medium-sized problems from the CUTE collection. [PUBLICATION ABSTRACT]
AbstractList We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush-Kuhn-Tucker point, an approximate Fritz-John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the [cursive l]2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without requiring linear independence constraint qualification, the algorithm is shown to be locally superlinearly convergent. The preliminary numerical results show that the algorithm is robust and efficient when solving some small- and medium-sized problems from the CUTE collection. [PUBLICATION ABSTRACT]
Author Yuan, Yaxiang
Liu, Xinwei
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Snippet We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In...
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SubjectTerms Algorithms
Applied mathematics
Computational mathematics
Mathematical functions
Methods
Optimization
Quadratic programming
Violations
Title A Sequential Quadratic Programming Method Without A Penalty Function or a Filter for Nonlinear Equality Constrained Optimization
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