A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods

Lateef Olakunle Jolaoso (), Adeolu Taiwo (), Timilehin Opeyemi Alakoya () and Oluwatosin Temitope Mewomo ()
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Lateef Olakunle Jolaoso: University of KwaZulu-Natal
Adeolu Taiwo: University of KwaZulu-Natal
Timilehin Opeyemi Alakoya: University of KwaZulu-Natal
Oluwatosin Temitope Mewomo: University of KwaZulu-Natal

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 4, 744-766

Abstract: Abstract Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.

Keywords: Variational inequality; Extragradient method; Fixed point problem; Projection method; Iterative method; Banach space; 65K15; 47J25; 65J15; 90C33 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-020-01672-3

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