Inertial extragradient type method for mixed variational inequalities without monotonicity

Lateef O. Jolaoso, Yekini Shehu*, Jen Chih Yao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we propose two inertial projection methods to solve mixed variational inequalities without assuming monotonicity on the cost operator. Consequently, we show that the sequence of iterates generated by our proposed methods converge globally to a solution of the mixed variational inequality under the condition that the set of solutions of the dual mixed variational inequality is nonempty. Our convergence results are obtained without assuming any further stringent condition imposed in other related results in the literature. Moreover, our results improve on many important related results in the literature. Some numerical illustrations are given to show the efficiency of our proposed methods.

Original languageEnglish
Pages (from-to)353-369
Number of pages17
JournalMathematics and Computers in Simulation
Volume192
DOIs
Publication statusPublished - Feb 2022

Keywords

  • Global convergence
  • Inertial terms
  • Mixed variational inequality
  • Projection method

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