Some characterizations of a nonlinear scalarizing function via oriented distance function. (16th December 2022)

• Record Type: Journal Article
• Authors: Han, Yu
• Is Part Of: Optimization. Volume 71:Number 16(2022)
• Page Start: 4785
• Page End: 4817
• Publication Date: 2022-12-16
• Subjects: Nonlinear scalarizing function -- oriented distance function -- convexity -- continuity -- Lipschitz continuity; 49J45 -- 49J53 -- 90C29 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1969392
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper aims at investigating some properties concerned with a nonlinear scalarizing function via oriented distance function. The convexity, continuity and Lipschitz continuity of the nonlinear scalarizing function are showed under some suitable conditions. As an application, we establish Lipschitz continuity of strongly approximate solution mapping for l -type order relation to parametric set optimization problems by using convexity and Lipschitz continuity of the nonlinear scalarizing function.