Two-level iterative method for non-stationary mixed variational inequalities
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We consider a mixed variational inequality problem involving a set-valued nonmonotone mapping and a general convex function, where only approximation sequences are known instead of exact values of the cost mapping and function, and feasible set. We suggest to apply a two-level approach with inexact solutions of each particular problem with a descent method and partial penalization and evaluation of accuracy with the help of a gap function. Its convergence is attained without concordance of penalty, accuracy, and approximation parameters under coercivity type conditions.
Keywordsmixed variational inequality >non-stationarity non-monotone mappings potential mappings approximate solutions penalty method gap function
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