A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

2006 ◽  
pp. 113-129 ◽  
Author(s):  
T. Q. Bao ◽  
P. Q. Khanh
Keyword(s):  
Variational Inequalities ◽  
Type Algorithm ◽  
Multivalued Variational Inequalities

scholarly journals On a class of multivalued variational inequalities

1998 ◽  
Vol 11 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Optimization Problems ◽  
Iterative Algorithms ◽  
Auxiliary Principle ◽  
Existence Of A Solution ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Projection Techniques ◽  
Multivalued Variational Inequalities

In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These variational inequalities include as special cases, the previously known classes of variational inequalities. Using projection techniques, we show that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of multivalued variational inequalities and suggest a novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.

scholarly journals Solving Yosida inclusion problem in Hadamard manifold

2019 ◽  
Vol 9 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Mohammad Dilshad
Keyword(s):  
Approximate Solution ◽  
Vector Field ◽  
Variational Inequalities ◽  
Hadamard Manifold ◽  
Inclusion Problem ◽  
Approximation Operator ◽  
Hadamard Manifolds ◽  
Yosida Approximation ◽  
Type Algorithm ◽  
Monotone Vector Field

Abstract We consider a Yosida inclusion problem in the setting of Hadamard manifolds. We study Korpelevich-type algorithm for computing the approximate solution of Yosida inclusion problem. The resolvent and Yosida approximation operator of a monotone vector field and their properties are used to prove that the sequence generated by the proposed algorithm converges to the solution of Yosida inclusion problem. An application to our problem and algorithm is presented to solve variational inequalities in Hadamard manifolds.

An extragradient-type algorithm for non-smooth variational inequalities

Optimization ◽  
2000 ◽  
Vol 48 (3) ◽  
pp. 309-332 ◽  
Author(s):  
Alfredo N Iusem ◽  
Luis R Lucambio Pérez
Keyword(s):  
Variational Inequalities ◽  
Type Algorithm
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