Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem. (25th July 2020)

• Record Type: Journal Article
• Authors: Han, Wenyan; Yu, Guolin; Gong, Tiantian
• Other Names: Hafstein Sigurdur F. Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-07-25
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/9849636
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.