Approximate solutions and scalarization in set-valued optimization. (2nd November 2017)

• Record Type: Journal Article
• Authors: Dhingra, Mansi; Lalitha, C. S.
• Is Part Of: Optimization. Volume 66:Number 11(2017)
• Page Start: 1793
• Page End: 1805
• Publication Date: 2017-11-02
• Subjects: Set-valued optimization -- approximate solutions -- scalarization -- Gerstewitz function -- Painlevé–Kuratowski convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1271419
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz's function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz's function are also established for approximate solutions, based on the lower set order relation.