Hölder Continuity of Solutions to Parametric Vector Equilibrium Problems with Nonlinear Scalarization

2014 ◽  
Vol 35 (6) ◽  
pp. 685-707 ◽  
Author(s):  
C. R. Chen ◽  
M. H. Li
Keyword(s):  
Equilibrium Problems ◽  
Hölder Continuity ◽  
Vector Equilibrium Problems ◽  
Holder Continuity ◽  
Nonlinear Scalarization ◽  
Continuity Of Solutions ◽  
Vector Equilibrium

scholarly journals A Note on Hölder Continuity of Solution Set for Parametric Vector Quasiequilibrium Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Xian-Fu Hu
Keyword(s):  
Metric Spaces ◽  
Equilibrium Problems ◽  
Hölder Continuity ◽  
Vector Equilibrium Problems ◽  
Holder Continuity ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Parametric Vector Quasiequilibrium Problems ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems

By using a scalarization technique, we extend and sharpen the results in S. Li and X. Li (2011) on the Hölder continuity of the solution sets of parametric vector equilibrium problems to the case of parametric vector quasiequilibrium problems in metric spaces. Furthermore, we also give an example to illustrate that our main results are applicable.

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.

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