Multi-valued variational inequalities with K-pseudomonotone operators

1994 ◽  
Vol 83 (2) ◽  
pp. 391-403 ◽  
Author(s):  
J. C. Yao
Keyword(s):  
Variational Inequalities ◽  
Pseudomonotone Operators

scholarly journals A class of nonlinear variational inequalities involving pseudomonotone operators

2000 ◽  
Vol 13 (1) ◽  
pp. 73-75
Author(s):  
Ram U. Verma
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Monotone Operators ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Pseudomonotone Operators ◽  
Topological Vector Spaces ◽  
Locally Convex

We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topological vector spaces setting. The obtained result generalizes similar variational inequality problems on monotone operators.

scholarly journals Proximal extragradient methods for pseudomonotone variational inequalities

2006 ◽  
Vol 37 (2) ◽  
pp. 109-116
Author(s):  
Muhammad Aslam Noor ◽  
Abdellah Bnouhachem
Keyword(s):  
Variational Inequalities ◽  
Iterative Methods ◽  
Proximal Methods ◽  
Pseudomonotone Operators ◽  
Extragradient Methods ◽  
Special Cases

We consider and analyze some new proximal extragradient type methods for solving variational inequalities. The modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. These new iterative methods include the projection, extragradient and proximal methods as special cases.

scholarly journals Iterative resolvent methods for general mixed variational inequalities

2003 ◽  
Vol 16 (3) ◽  
pp. 283-294
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problems ◽  
Splitting Methods ◽  
Pseudomonotone Operators ◽  
Special Cases ◽  
Mixed Variational Inequalities ◽  
Proof Of Convergence ◽  
Self Adaptive

In this paper, we use the technique of updating the solution to suggest and analyze a class of new self-adaptive splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Proof of convergence is very simple. Since general mixed variational include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.

scholarly journals Forward-backward resolvent splitting methods for general mixed variational inequalities

2003 ◽  
Vol 2003 (43) ◽  
pp. 2759-2770
Author(s):  
Muhammad Aslam Noor ◽  
Muzaffar Akhter ◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problems ◽  
Splitting Methods ◽  
Pseudomonotone Operators ◽  
Special Cases ◽  
Mixed Variational Inequalities

We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known three-step forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for solving various classes of variational inequalities and complementarity problems. Since general mixed variational inequalities include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.

scholarly journals A Tseng-Type Algorithm with Self-Adaptive Techniques for Solving the Split Problem of Fixed Points and Pseudomonotone Variational Inequalities in Hilbert Spaces

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 152
Author(s):  
Li-Jun Zhu ◽  
Yeong-Cheng Liou
Keyword(s):  
Variational Inequalities ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Pseudomonotone Operators ◽  
Adaptive Techniques ◽  
Type Algorithm ◽  
Self Adaptive

In this paper, we survey the split problem of fixed points of two pseudocontractive operators and variational inequalities of two pseudomonotone operators in Hilbert spaces. We present a Tseng-type iterative algorithm for solving the split problem by using self-adaptive techniques. Under certain assumptions, we show that the proposed algorithm converges weakly to a solution of the split problem. An application is included.

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