The formulas for the representation of functions of two variables as a difference of sublinear functions. (3rd October 2019)

• Record Type: Journal Article
• Authors: Grzybowski, Jerzy; Pallaschke, Diethard; Urbański, Ryszard
• Is Part Of: Optimization. Volume 68:Number 10(2019)
• Page Start: 2055
• Page End: 2070
• Publication Date: 2019-10-03
• Subjects: Differences of sublinear functions (ds-functions) -- minimal representation of ds-function -- support functions -- subdifferential and superdifferential; 26B25 -- 49J52 -- 52A10 -- 54C35; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1491572
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Having a function being a difference of sublinear functions defined on a plane, we present a formula for effective calculation of sublinear functions such that their difference is equal to the given one. Moreover, these newly calculated sublinear functions are minimal and as such unique-up-to-linear-summand. We also provide examples of such functions.