Optimization of one class of nonsymmetrizable algorithms for saddle point problems

Abstract

To solve the nondegenerate system of linear special-type equations we consider a threeparameter algorithm which is a generalization of the known Arrow-Hurwicz algorithm. For the proposed algorithm we solve an asymptotic optimization problem in two different statements. We obtain analytic formulae for asymptotically optimal parameters and the convergence factor. The results obtained are of an unimprovable character for the studied class of algorithms.