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

AbstractGiven an arbitrary point (x, u) inRn× 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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