LP well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints
type: Item
instance of: scholarly article
title: LP well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints
zbMATH Open document ID: 1474.90461
DOI: 10.1155/2014/792984
author: Phan Quoc Khanh
author: Kamonrat Sombut
author: Somyot Plubtieng
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 7023083
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/792984
OpenAlex ID: W2024357668
Wikidata QID: Q59041529
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description: scientific article; zbMATH DE number 7023083