Global optimization of the difference of affine increasing and positively homogeneous functions. (1st December 2016)

• Record Type: Journal Article
• Authors: Mohebi, Atefeh; Mohebi, Hossein
• Is Part Of: Optimization. Volume 65:Number 12(2016)
• Page Start: 2081
• Page End: 2093
• Publication Date: 2016-12-01
• Subjects: Monotonic analysis -- increasing and positively homogeneous function -- affine IPH function -- support set -- maximal element -- global minimum -- abstract convexity; 90C46 -- 26B25 -- 26A48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1227807
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The theory of increasing and positively homogeneous (IPH) functions defined on a real topological vector space X has well been developed. In this paper, we first give various characterizations for maximal elements of the support set of this class of functions. As an application, we present various characterizations for maximal elements of the support set of affine IPH functions. Finally, we investigate necessary and sufficient conditions for the global minimum of the difference of two strictly affine IPH functions.