## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 792984, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606035

Digital Object Identifier
doi:10.1155/2014/792984

Mathematical Reviews number (MathSciNet)
MR3198250

Zentralblatt MATH identifier
07023083

#### Citation

Khanh, Phan Quoc; Plubtieng, Somyot; Sombut, Kamonrat. LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 792984, 7 pages. doi:10.1155/2014/792984. https://projecteuclid.org/euclid.aaa/1412606035

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