Auxiliary Principle and Iterative Algorithms for Generalized Set-Valued Strongly Nonlinear Mixed Variational-like Inequalities☆

By Nan-Jing Huang, Chuanxian Deng. 2001

93 citations recorded by the source corpus.

In this paper, we extend the auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities. We prove the existence of a solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities, construct the iterative algorithm for the generalized set-valued strongly nonlinear mixed variational-like inequalities, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed variational-like inequality by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/60dad1f569a0492abb8f744e88208c036b598377

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Citations in the corpus

Invex equilibrium problems (2005, methodology): “2) and its variant forms have been studied extensively by many authors in the setting of convexity using the KKM mappings and fixed-point theory, see [6–12] and the references therein.”
A new class of general variational inclusions involving maximal $\eta$-monotone mappings (2003, background): “It is known that a number of problems involving the nonmonotone, nonconvex, and nonsmooth mappings arising in structural engineering, mechanics, economics, and optimization theory can be reduced to study this kind of variational inclusions (see, for example, [2], [5], [11], [17], [20]).”