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<p>This article delves into the analysis of semi-infinite multi-objective optimization problems characterized by constraints that gradually vanish. We establish sufficient efficiency criteria to determine whether a feasible solution attains a Pareto solution in the given multi-objective optimization problem considering the presence of vanishing constraints and suitable generalized convexity assumptions. We provide illustrative examples to confirm the validity of our findings. Additionally, we derive weak, converse, strong converse, and strong duality theorems for a dual model based on Mond–Weir principles, relying on generalized convexity assumptions.</p>

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Efficiency criteria and dual models for multi-objective semi-infinite constrained minimization problems with vanishing restrictions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月4日

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  • Murari Kumar Roy,
  • Bhuwan Chandra Joshi,
  • Savin Treanţă,
  • Cristina-Florentina Marghescu

摘要

This article delves into the analysis of semi-infinite multi-objective optimization problems characterized by constraints that gradually vanish. We establish sufficient efficiency criteria to determine whether a feasible solution attains a Pareto solution in the given multi-objective optimization problem considering the presence of vanishing constraints and suitable generalized convexity assumptions. We provide illustrative examples to confirm the validity of our findings. Additionally, we derive weak, converse, strong converse, and strong duality theorems for a dual model based on Mond–Weir principles, relying on generalized convexity assumptions.