Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem

1997 ◽  
Vol 93 (1) ◽  
pp. 141-151 ◽  
Author(s):  
J. Fu
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problem ◽  
Vector Variational Inequalities ◽  
Implicit Complementarity Problem

scholarly journals On the implicit complementarity problem in Hilbert spaces

1985 ◽  
Vol 32 (2) ◽  
pp. 251-260 ◽  
Author(s):  
G. Isac
Keyword(s):  
Optimal Control ◽  
Variational Inequalities ◽  
Existence Theorem ◽  
Hilbert Spaces ◽  
Stochastic Optimal Control ◽  
Complementarity Problem ◽  
Principal Result ◽  
Implicit Complementarity Problem

We consider in this paper the implicit complementarity problem imposed by quasi-variational inequalities and stochastic optimal control. The principal result is an existence theorem for the implicit complementarity problem in Hilbert spaces.

scholarly journals Vector variational inequalities and their relations with vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Surjeet Kaur Suneja ◽  
Bhawna Kohli
Keyword(s):  
Variational Inequalities ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Clarke Subdifferential ◽  
Vector Variational Inequalities ◽  
Regularity Assumption ◽  
Weak Minimum ◽  
Minimum Solution ◽  
Clarke Subdifferentials

In this paper, K- quasiconvex, K- pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where   is an arbitrary closed convex, pointed cone with nonempty interior. The (strict, weakly) -pseudomonotonicity, (strict) K- naturally quasimonotonicity and K- quasimonotonicity of Clarke subdifferential maps have also been defined. Further, we introduce Minty weak (MVVIP) and Stampacchia weak (SVVIP) vector variational inequalities over arbitrary cones. Under regularity assumption, we have proved that a weak minimum solution of vector optimization problem (VOP) is a solution of (SVVIP) and under the condition of K- pseudoconvexity we have obtained the converse for MVVIP (SVVIP). In the end we study the interrelations between these with the help of strict K-naturally quasimonotonicity of Clarke subdifferential map.

Modulus-based Synchronous Multisplitting Iteration Methods for an Implicit Complementarity Problem

2017 ◽  
Vol 7 (2) ◽  
pp. 363-375 ◽  
Author(s):  
Chen-Liang Li ◽  
Jun-Tao Hong
Keyword(s):  
Theoretical Analysis ◽  
Complementarity Problem ◽  
Numerical Results ◽  
Multiprocessor Systems ◽  
Implicit Complementarity Problem ◽  
New Methods ◽  
Iteration Methods

AbstractWe construct modulus-based synchronous multisplitting iteration methods to solve a large implicit complementarity problem on parallel multiprocessor systems, and prove their convergence. Numerical results confirm our theoretical analysis and show that these new methods are efficient.

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