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Abstract and Applied Analysis
Volume 2014, Article ID 792984, 7 pages
http://dx.doi.org/10.1155/2014/792984
Research Article

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

1Department of Mathematics, International University of Ho Chi Minh City, Linh Trung, Thu Duc, Ho Chi Minh City, Vietnam
2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 21 January 2014; Accepted 9 March 2014; Published 17 April 2014

Academic Editor: Chong Li

Copyright © 2014 Phan Quoc Khanh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.