A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems

2005 ◽  
Vol 32 (4) ◽  
pp. 451-466 ◽  
Author(s):  
G. Y. Chen ◽  
X. Q. Yang ◽  
H. Yu
Keyword(s):  
Equilibrium Problems ◽  
Vector Equilibrium Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function ◽  
Vector Equilibrium

scholarly journals LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Phan Quoc Khanh ◽  
Somyot Plubtieng ◽  
Kamonrat Sombut
Keyword(s):  
Equilibrium Problems ◽  
Optimization Problems ◽  
Well Posedness ◽  
Equilibrium Constraints ◽  
Vector Equilibrium Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Measures Of Noncompactness ◽  
Scalarization Function ◽  
Vector Equilibrium

The purpose of this paper is introduce several types of Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Base on criterion and characterizations for these types of Levitin-Polyak well-posedness we argue on diameters and Kuratowski’s, Hausdorff’s, or Istrǎtescus measures of noncompactness of approximate solution sets under suitable conditions, and we prove the Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Obtain a gap function for bilevel vector equilibrium problems with equilibrium constraints using the nonlinear scalarization function and consider relations between these types of LP well-posedness for bilevel vector optimization problems with equilibrium constraints and these types of Levitin-Polyak well-posedness for bilevel vector equilibrium problems with equilibrium constraints under suitable conditions; we prove the Levitin-Polyak well-posedness for bilevel equilibrium and optimization problems with equilibrium constraints.

scholarly journals Constrained Weak Nash-Type Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
W. C. Shuai ◽  
K. L. Xiang ◽  
W. Y. Zhang
Keyword(s):  
Existence Theorem ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function ◽  
Payoff Functions

A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. The results extend the corresponding one of Fu (2003). In particular, if the payoff functions are singlevalued, our existence theorem extends the main results of Fu (2003) by relaxing the assumption of convexity.

scholarly journals Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei-bing Zhang ◽  
Nan-jing Huang ◽  
Donal O’Regan
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

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