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

Author

Listed:
  • 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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:792984
    DOI: 10.1155/2014/792984
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