Proper efficiency, scalarization and transformation in multi-objective optimization: unified approaches. (4th March 2022)

• Record Type: Journal Article
• Authors: Zamani, Moslem; Soleimani-damaneh, Majid
• Is Part Of: Optimization. Volume 71:Number 3(2022)
• Page Start: 753
• Page End: 774
• Publication Date: 2022-03-04
• Subjects: Multi-objective optimization -- proper efficiency -- scalarization -- transformation; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1812602
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar program are properly efficient and vice versa. We also show that, under some conditions, if the considered general scalar problem is unbounded, then the original multi-objective problem does not have any properly efficient solution. In another part of the work, we investigate a general transformation of the objective functions which preserves proper efficiency. We show that several important results existing in the literature are direct consequences of the results of the present paper.