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.
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Communicated by P. Kall
Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based on research sponsored by National Science Foundation Grant No. DCR-8420963 and Air Force Office of Scientific Research Grant No. AFOSR-ISSA-85-00080.
On leave from CRAI, via Bernini 5, Rende, Cosenza, Italy.
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Mangasarian, O.L., De Leone, R. Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs. Appl Math Optim 17, 1–14 (1988). https://doi.org/10.1007/BF01448356
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DOI: https://doi.org/10.1007/BF01448356