A New Algorithm for Solving Strictly Convex Quadratic Programs

We reformulate convex quadratic programs with simple bound constraints and strictly convex quadratic programs as problems of unconstrained minimization of convex quadratic splines. Therefore, any algorithm for finding a minimizer of a convex quadratic spline can be used to solve these quadratic prog...

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Veröffentlicht in:SIAM journal on optimization Jg. 7; H. 3; S. 595 - 619
Hauptverfasser: Li, Wu, Swetits, John
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.08.1997
Schlagworte:
Algorithms
Approximation
Linear equations
Methods
ISSN:1052-6234, 1095-7189
Online-Zugang:Volltext
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Zusammenfassung:We reformulate convex quadratic programs with simple bound constraints and strictly convex quadratic programs as problems of unconstrained minimization of convex quadratic splines. Therefore, any algorithm for finding a minimizer of a convex quadratic spline can be used to solve these quadratic programming problems. In this paper, we propose a Newton method to find a minimizer of a convex quadratic spline derived from the unconstrained reformulation of a strictly convex quadratic programming problem. The Newton method is a "natural mixture" of a descent method and an active-set method. Moreover, it is an iterative method, yet it terminates in finite operations (in exact arithmetic).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623493246045