Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 8 2 2024 11 18 An Extension of the Min-Max Method for Approximate Solutions of Multiobjective Optimization Problems 202 211 441 10.22128/gadm.2024.858.1117 EN Hossein Salmei Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Mehran Namjoo Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran 0000-0001-5949-6766 Journal Article 2024 08 06 ‎It is a common characteristic of many multiobjective optimization problems that the efficient solution set can only be identified approximately‎. ‎This study addresses scalarization techniques for solving multiobjective optimization problems‎. ‎The min-max scalarization technique is considered‎, ‎and efforts are made to overcome its weaknesses in studying approximate efficient solutions‎. ‎To this end‎, ‎two modifications of the min-max scalarization technique are proposed‎. ‎First‎, ‎an alternative form of the min-max method is introduced‎. ‎Additionally‎, ‎by using slack and surplus variables in the constraints and penalizing violations in the objective function‎, ‎we obtain easy-to-check conditions for approximate efficiency‎. ‎The established theorems clarify the relationship between $\varepsilon$-(weakly and properly) efficient solutions of the multiobjective optimization problem and $\epsilon$-optimal solutions of the proposed scalarized problems‎, ‎without requiring any assumptions of convexity. https://ansne.du.ac.ir/article_441_3ac0fda3f57295d46d8e30eeb59c4d29.pdf