scholarly journals Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints

2008 ◽  
Vol 55 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Ya-Ping Fang ◽  
Rong Hu ◽  
Nan-Jing Huang
Keyword(s):  
Equilibrium Problems ◽  
Optimization Problems ◽  
Well Posedness ◽  
Equilibrium Constraints

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 New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-1 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Lai-Jiu Lin ◽  
Gue Myung Lee ◽  
Tamaki Tanaka
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Fixed Point Theory ◽  
Point Theory
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