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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Bibliographic Details
Published in:SIAM journal on optimization Vol. 7; no. 3; pp. 595 - 619
Main Authors: Li, Wu, Swetits, John
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.08.1997
Subjects:
Algorithms
Approximation
Linear equations
Methods
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary: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).
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ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623493246045