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

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Abstract

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.

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Authors and Affiliations

  1. Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    I. V. Konnov

  2. Jazan University, Jazan, Saudi Arabia

    Salahuddin

Authors
  1. I. V. Konnov
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  2. Salahuddin
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Correspondence to I. V. Konnov.

Additional information

Original Russian Text © I.V. Konnov, Salahuddin, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 10, pp. 50–61.

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Konnov, I.V., Salahuddin Two-level iterative method for non-stationary mixed variational inequalities. Russ Math. 61, 44–53 (2017). https://doi.org/10.3103/S1066369X17100061

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  • DOI: https://doi.org/10.3103/S1066369X17100061

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