Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized ( F, α, ρ, d )- I -Type Invex Functions

Rongbo Wang and Qiang Feng ()
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Rongbo Wang: School of Mathematics and Computer Science, Yanan University, Yanan 716000, China
Qiang Feng: School of Mathematics and Computer Science, Yanan University, Yanan 716000, China

Mathematics, 2024, vol. 12, issue 16, 1-13

Abstract: Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on the theory and application of convex functions and their generalized convexity in multiobjective programming helps us understand the essence of optimization problems, and promotes the development of optimization algorithms and theories. In this paper, we firstly introduces new classes of generalized ( F , α , ρ , d ) − I functions for semi-preinvariant convex multiobjective programming. Secondly, based on these generalized functions, we derive several sufficient optimality conditions for a feasible solution to be an efficient or weakly efficient solution. Finally, we prove weak duality theorems for mixed-type duality.

Keywords: semi-preinvariant convexity; multiobjective programming; efficient solution; generalized convexity; mixed-type duality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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