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Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs

Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for... Given an arbitrary point (x, u) inR n × R + m , we give bounds on the Euclidean distance betweenx and the unique solution $$\bar x$$ to a strongly convex program in terms of the violations of the Karush-Kuhn-Tucker conditions by the arbitrary point (x, u). These bounds are then used to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least 2-norm solution of a linear program. These schemes can be used effectively in conjunction with the successive overrelaxation (SOR) methods for solving very large sparse linear programs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 1988 by Springer-Verlag New York Inc
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01448356
Publisher site
See Article on Publisher Site

Abstract

Given an arbitrary point (x, u) inR n × R + m , we give bounds on the Euclidean distance betweenx and the unique solution $$\bar x$$ to a strongly convex program in terms of the violations of the Karush-Kuhn-Tucker conditions by the arbitrary point (x, u). These bounds are then used to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least 2-norm solution of a linear program. These schemes can be used effectively in conjunction with the successive overrelaxation (SOR) methods for solving very large sparse linear programs.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Mar 23, 2005

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