Gap functions and error bounds for nonsmooth convex vector optimization problem. (2nd November 2017)

• Record Type: Journal Article
• Authors: Dutta, Joydeep; Kesarwani, Poonam; Gupta, Sanjeev
• Is Part Of: Optimization. Volume 66:Number 11(2017)
• Page Start: 1807
• Page End: 1836
• Publication Date: 2017-11-02
• Subjects: Convex functions -- convex optimization -- vector optimization -- subdifferential -- gap function -- error bounds; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1332622
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this article, our main aim is to develop gap functions and error bounds for a (non-smooth) convex vector optimization problem. We show that by focusing on convexity we are able to quite efficiently compute the gap functions and try to gain insight about the structure of set of weak Pareto minimizers by viewing its graph. We will discuss several properties of gap functions and develop error bounds when the data are strongly convex. We also compare our results with some recent results on weak vector variational inequalities with set-valued maps, and also argue as to why we focus on the convex case.