Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs (Q1103527)

For strongly convex programs error bounds on the Euclidean distance between x and the unique optimal solution \(\bar x\) are derived in terms of the violation of the Karush-Kuhn-Tucker conditions by an arbitrary point \((x,u)\in R^ n\times R^ m_+\). These bounds are uses to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least \(\ell_ 2\)-norm solution of a linear program. These algorithms can effectively be used in connection with successive overrelaxation (SOR) methods for solving very large sparse linear programs.