scholarly journals Solving Mixed Variational Inequalities Beyond Convexity

2021 ◽  
Author(s):  
Sorin-Mihai Grad ◽  
Felipe Lara
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Numerical Experiments ◽  
Golden Ratio ◽  
Mixed Variational Inequalities

AbstractWe show that Malitsky’s recent Golden Ratio Algorithm for solving convex mixed variational inequalities can be employed in a certain nonconvex framework as well, making it probably the first iterative method in the literature for solving generalized convex mixed variational inequalities, and illustrate this result by numerical experiments.

NEW THREE-STEP ITERATIVE METHOD FOR SOLVING MIXED VARIATIONAL INEQUALITIES

2011 ◽  
Vol 08 (01) ◽  
pp. 139-150
Author(s):  
ABDELLAH BNOUHACHEM ◽  
MUHAMMAD ASLAM NOOR ◽  
ZHAOHAN SHENG ◽  
EISA AL-SAID
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Numerical Experiments ◽  
New Method ◽  
Descent Direction ◽  
Mild Conditions ◽  
Globally Convergent ◽  
Special Cases ◽  
Mixed Variational Inequalities

In this paper, we suggest and analyze a new three-step iterative method for solving mixed variational inequalities. The new iterate is obtained by using a descent direction. We prove that the new method is globally convergent under suitable mild conditions. Our results can be viewed as significant extensions of the previously known results for mixed variational inequalities. Since mixed variational inequalities include variational inequalities as special cases, our method appears to be a new one for solving variational inequalities. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.

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