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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2017 Number 10, Pages 50–61 (Mi ivm9289)

This article is cited in 6 papers

Two-level iterative method for non-stationary mixed variational inequalities

I. V. Konnova, Salahuddinb

a Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
b Jazan University, Jazan, K. S. A.

Abstract: We consider a mixed variational inequality problem involving a set-valued non-monotone 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.

Keywords: mixed variational inequality, non-stationarity, non-monotone mappings, potential mappings, approximate solutions, penalty method, gap function.

UDC: 519.852

Received: 03.06.2016


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:10, 44–53

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