Abstract
In this paper, we study the duality theorems of a nondifferentiable semi-infinite interval-valued optimization problem with vanishing constraints (IOPVC). By constructing the Wolfe and Mond–Weir type dual models, we give the weak duality, strong duality, converse duality, restricted converse duality, and strict converse duality theorems between IOPVC and its corresponding dual models under the assumptions of generalized convexity.
Highlights
In recent years, the mathematical programming problems with vanishing constraints (MPVCs) have been studied extensively by many scholars
Achtziger and Kanzow [1] first proposed an optimization problem with vanishing constraints (MPVCs) and gave the strong stationary point theorem and VC-stationary point theorem of MPVCs under Abadie constraint qualification (ACQ) and improved ACQ assumptions
The study of dual problems related to MPVCs has been used as a tool to solve optimization problems in various fields in the past decades, such as variational problems, fractional programming problems, semi-infinite programming problems, complex minimax problems, and so on
Summary
The mathematical programming problems with vanishing constraints (MPVCs) have been studied extensively by many scholars. Theorem 2.1 Let x ∈ E be a locally weakly LU optimal solution of (IOPVC) such that (VC-ACQ) holds at xand
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