Continuity of the efficient solution mapping for vector optimization problems. (2nd July 2016)

• Record Type: Journal Article
• Authors: Han, Yu; Gong, Xunhua
• Is Part Of: Optimization. Volume 65:Number 7(2016)
• Page Start: 1337
• Page End: 1347
• Publication Date: 2016-07-02
• Subjects: Vector optimization -- efficient solution -- upper semicontinuity -- lower semicontinuity -- strictly cone-quasiconvexity; 90C26 -- 90C29 -- 90C30 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1154554
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper aims at investigating the continuity of the efficient solution mapping of perturbed vector optimization problems. First, we introduce the concept of the level mapping. We give sufficient conditions for the upper semicontinuity and the lower semicontinuity of the level mapping. The upper semicontinuity and the lower semicontinuity of the efficient solution mapping are established by using the continuity properties of the level mapping. We establish a corollary about the lower semicontinuity of the minimal point set-valued mapping. Meanwhile, we give some examples to illustrate that the corollary is different from the ones in the literature.