Noncoercive variational inequalities for pseudomonotone operators

1991 ◽  
Vol 61 (1) ◽  
pp. 141-183 ◽  
Author(s):  
Franco Tomarelli
Keyword(s):  
Variational Inequalities ◽  
Pseudomonotone Operators ◽  
Noncoercive Variational Inequalities

Recession mappings and noncoercive variational inequalities

1996 ◽  
Vol 26 (9) ◽  
pp. 1573-1603 ◽  
Author(s):  
Samir Adly ◽  
Daniel Goeleven ◽  
Michel Théra
Keyword(s):  
Variational Inequalities ◽  
Noncoercive Variational Inequalities

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.

Noncoercive variational inequalities with application to friction problems

1991 ◽  
Vol 117 (3-4) ◽  
pp. 275-293 ◽  
Author(s):  
P. Shi ◽  
M. Shillor
Keyword(s):  
Variational Inequalities ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Obstacle Problems ◽  
Elastic Contact ◽  
Compatibility Conditions ◽  
Sublinear Functionals ◽  
Noncoercive Variational Inequalities ◽  
Necessary And Sufficient

SynopsisNoncoercive variational inequalities with sublinear functionals are considered. Necessary and sufficient conditions are given for the solvability of such problems. These conditions are in the form of compatibility conditions-for the data, as well as the boundedness of the solutions to related problems. These results are used for the obstacle problems for the membrance and the elastic contact in the presence of friction.

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.

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