Exceptional Family of Elements for a Variational Inequality Problem and its Applications

Authors:
Y. B. Zhao;J. Han
Affiliations:
Institute of Applied Mathematics, Chinese Academy of Sciences, P.O. Box 2734, Beijing, 100080, People‘s Republic of China (e-mail: zyb@lsec.cc.ac.cn);Institute of Applied Mathematics, Chinese Academy of Sciences, P.O. Box 2734, Beijing, 100080, People‘s Republic of China (e-mail: zyb@lsec.cc.ac.cn)
Venue:
Journal of Global Optimization
Year:
1999

Citing 12
Cited 6

A note on the existence of traffic equilibria

Applied Mathematics and Computation
Seven kinds of monotone maps

Journal of Optimization Theory and Applications
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
Solution of P0-matrix linear complementarity problems using a potential reduction algorithm

SIAM Journal on Matrix Analysis and Applications
On a Generalization of a Normal Map and Equation

SIAM Journal on Control and Optimization
A quadratically convergent Ok+1 nL -iteration algorithm for the P*k -matrix linear complementarity problem

Mathematical Programming: Series A and B
Predictor-corrector algorithm for solving P*(&kgr;)-matrix LCP from arbitrary positive starting points

Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Exceptional families and finite-dimensional variational inequalities over polyhedral convex sets

Applied Mathematics and Computation
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
A Large-Step Infeasible-Interior-Point Method for the P*-Matrix LCP

SIAM Journal on Optimization
A Quadratically Convergent Infeasible-Interior-Point Algorithm for LCP with Polynomial Complexity

SIAM Journal on Optimization
Exceptional Families, Topological Degree and Complementarity Problems

Journal of Global Optimization

Duality in Multivalued Complementarity Theory by Using Inversions and Scalar Derivatives

Journal of Global Optimization
Solving variational inequalities defined on a domain with infinitely many linear constraints

Computational Optimization and Applications
Exceptional family of elements for generalized variational inequalities

Journal of Global Optimization
Solvability of implicit complementarity problems

Mathematical and Computer Modelling: An International Journal
Existence of a solution to nonlinear variational inequality under generalized positive homogeneity

Operations Research Letters
Generalization of an existence theorem for complementarity problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper introduces a new concept of exceptional family of elements (abbreviated, exceptional family) for a finite-dimensional nonlinear variational inequality problem. By using this new concept, we establish a general sufficient condition for the existence of a solution to the problem. Such a condition is used to develop several new existence theorems. Among other things, a sufficient and necessary condition for the solvability of pseudo-monotone variational inequality problem is proved. The notion of coercivity of a function and related classical existence theorems for variational inequality are also generalized. Finally, a solution condition for a class of nonlinear complementarity problems with so-called P_*-mappings is also obtained.