Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications

Yu Han () and Nan-jing Huang ()
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Yu Han: Sichuan University
Nan-jing Huang: Sichuan University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 6, 679-695

Abstract: Abstract Hern $$\acute{\mathrm{a}}$$ a ´ ndez and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) introduced a nonlinear scalarizing function for sets, which is a generalization of the Gerstewitz’s function. This paper aims at investigating some properties concerned with the nonlinear scalarizing function for sets. The continuity and convexity of the nonlinear scalarizing function for sets are showed under some suitable conditions. As applications, the upper semicontinuity and the lower semicontinuity of strongly approximate solution mappings to the parametric set optimization problems are also given.

Keywords: Set optimization problem; Nonlinear scalarizing function; Continuity; Convexity; 49J53; 90C29 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10957-017-1080-9

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