The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K,ρ )−Invexity

Hong Yang () and Angang Cui
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Hong Yang: School of Mathematics and Statistics, Yulin University, Yulin 719000, China
Angang Cui: School of Mathematics and Statistics, Yulin University, Yulin 719000, China

Mathematics, 2023, vol. 11, issue 20, 1-13

Abstract: Minimax fractional semi-infinite programming is an important research direction for semi-infinite programming, and has a wide range of applications, such as military allocation problems, economic theory, cooperative games, and other fields. Convexity theory plays a key role in many aspects of mathematical programming and is the foundation of mathematical programming research. The relevant theories of semi-infinite programming based on different types of convex functions have their own applicable scope and limitations. It is of great value to study semi-infinite programming on the basis of more generalized convex functions and obtain more general results. In this paper, we defined a new type of generalized convex function, based on the concept of the K −directional derivative, that is, uniform ( B K , ρ ) − invex, strictly uniform ( B K , ρ ) − invex, uniform ( B K , ρ ) − pseudoinvex, strictly uniform ( B K , ρ ) − pseudoinvex, uniform ( B K , ρ ) − quasiinvex and weakly uniform ( B K , ρ ) − quasiinvex function. Then, we studied a class of non-smooth minimax fractional semi-infinite programming problems involving this generalized convexity and obtained sufficient optimality conditions.

Keywords: non-smooth programming; fractional semi-infinite programming; K ?directional derivative; uniform ( B K , ? )?invexity; optimality conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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