1. LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints.
- Author
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Phan Quoc Khanh, Somyot Plubtieng, and Kamonrat Sombut
- Subjects
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MATHEMATICAL optimization , *NASH equilibrium , *COMPLEMENTARITY constraints (Mathematics) , *MATHEMATICAL functions , *DIFFERENTIAL equations , *MATHEMATICAL analysis - Abstract
The purpose of this paper is introduce several types of Levitin-Polyakwell-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. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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