Abstract
In this paper, we introduce a new class of generalized strongly set‐valued nonlinear complementarity problems and construct new iterative algorithms. We show the existence of solutions for this kind of nonlinear complementarity problems and the convergence of iterative sequences generated by the algorithm. Our results extend some recent results in this field.
Highlights
The complementarity theory, which was introduced by Lemke [11], Cottle, and Dantzig [6] in the early 1960s and later developed by others, plays an important and fundamental role in the study of a wide class of problems arising in mechanics, physics, control and optimization, economics and transportation equilibrium, contact problems in elasticity, fluid flow through porous media, and many other branches of mathematical and engineering sciences [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15]
We introduce and study a new class of generalized strongly set-valued nonlinear complementarity problems and construct new iterative algorithms
We discuss the existence of solutions for this kind of nonlinear complementarity problems and the convergence of iterative sequences generated by the algorithm
Summary
The complementarity theory, which was introduced by Lemke [11], Cottle, and Dantzig [6] in the early 1960s and later developed by others, plays an important and fundamental role in the study of a wide class of problems arising in mechanics, physics, control and optimization, economics and transportation equilibrium, contact problems in elasticity, fluid flow through porous media, and many other branches of mathematical and engineering sciences [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15]. The set-valued quasi-(implicit)complementarity problems, considered and studied by Chang and Huang [2, 3], are important among the generalizations of the complementarity problems. We introduce and study a new class of generalized strongly set-valued nonlinear complementarity problems and construct new iterative algorithms.
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