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Inexact proximal point method for general variational inequalities. (English) Zbl 1101.49026
Summary: We suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.
MSC:
49M37Methods of nonlinear programming type in calculus of variations
49J40Variational methods including variational inequalities