scholarly journals Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities

2020 ◽  
Vol 16 (3) ◽  
pp. 1261-1272
Author(s):  
Minghua Li ◽  
◽  
Chunrong Chen ◽  
Shengjie Li ◽  
Keyword(s):  
Error Bounds ◽  
Gap Functions ◽  
Ky Fan Inequalities ◽  
Regularized Gap Functions ◽  
Ky Fan

scholarly journals Continuity Results and Error Bounds on Pseudomonotone Vector Variational Inequalities via Scalarization

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Xin Zuo ◽  
Hong-Zhi Wei ◽  
Chun-Rong Chen
Keyword(s):  
Variational Inequality ◽  
Error Bounds ◽  
Vector Variational Inequality ◽  
Gap Functions ◽  
Strong Pseudomonotonicity ◽  
Solution Mapping ◽  
Constraint Set ◽  
Regularized Gap Functions ◽  
Lower And Upper Semicontinuities ◽  
Weak Vector

Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions.

scholarly journals Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone

2021 ◽  
Author(s):  
Nguyen Van Hung ◽  
Vicente Novo ◽  
Vo Minh Tam
Keyword(s):  
Partial Order ◽  
Error Bounds ◽  
Equilibrium Problems ◽  
Polyhedral Cone ◽  
Gap Functions ◽  
Vector Equilibrium Problems ◽  
Error Bound Analysis ◽  
Vector Equilibrium ◽  
Vector Valued Function ◽  
Regularized Gap Functions

AbstractThe aim of this paper is to establish new results on the error bounds for a class of vector equilibrium problems with partial order provided by a polyhedral cone generated by some matrix. We first propose some regularized gap functions of this problem using the concept of $$\mathcal {G}_{A}$$ G A -convexity of a vector-valued function. Then, we derive error bounds for vector equilibrium problems with partial order given by a polyhedral cone in terms of regularized gap functions under some suitable conditions. Finally, a real-world application to a vector network equilibrium problem is given to illustrate the derived theoretical results.

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