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

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  • Phan Quoc Khanh
  • Somyot Plubtieng
  • Kamonrat Sombut

Abstract

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.

Suggested Citation

  • Phan Quoc Khanh & Somyot Plubtieng & Kamonrat Sombut, 2014. "LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    • Handle: RePEc:hin:jnlaaa:792984
    DOI: 10.1155/2014/792984
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