A vector auxiliary principle technique approach to systems of mixed vector equilibrium problems

Optimization ◽  
2018 ◽  
Vol 69 (2) ◽  
pp. 221-241 ◽  
Author(s):  
Ouayl Chadli ◽  
Asma Saidi ◽  
Xiaopeng Zhao
Keyword(s):  
Equilibrium Problems ◽  
Vector Equilibrium Problems ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Vector Equilibrium

scholarly journals Mixed quasi invex equilibrium problems

2004 ◽  
Vol 2004 (57) ◽  
pp. 3057-3067 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Strong Monotonicity ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Iterative Schemes ◽  
New Class ◽  
Special Cases ◽  
Weaker Conditions

We introduce a new class of equilibrium problems, known asmixed quasi invex equilibrium(orequilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle technique. It is shown that the convergence of these iterative schemes requires either pseudomonotonicity or partially relaxed strong monotonicity, which are weaker conditions than the previous ones. As special cases, we also obtained the correct forms of the algorithms for solving variational-like inequalities, which have been considered in the setting of convexity. In fact, our results represent significant and important refinements of the previously known results.

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