Title: Nonconvex Bifunction General Variational Inequalities
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-20-00052; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 1-8
Document Type: Research Paper
Author(s): Muhammad Aslam Noor a , Khalida Inayat Noor
b
aDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
bDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
Received: 23 December 2020, Accepted: 18 February 2021, Published: 8 May 2021.
Corresponding Author: Muhammad Aslam Noor (Email address: noormaslam@gmail.com)
Full Text: PDF
Abstract
In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex bifunction general variational inequality. Using the auxiliary principle technique, we suggest and analyze some iterative methods for solving the nonconvex bifunction general variational inequalities. We prove that the convergence of these methods either requires only pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. The ideas and techniques of this paper may stimulate further research in this field.
Keywords: Convex programming, Nonlinear programming, Bifunction variational inequalities, Nonconvex functions, Auxiliary principle technique, Convergence
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