Approximate proper solutions in vector optimization with variable ordering structure

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 14، Issue 1 - شماره پیاپی 28، خرداد 2024، صفحه 107-135   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.83112.1288

نویسنده

S. Shahbeyk^*

Department of Mathematics, Faculty of Statistics, Mathematics, and Computer Science, Allameh Tabataba’i University , Tehran, Iran.

چکیده

In this paper, we study approximate proper efficient (nondominated and minimal) solutions of vector optimization problems with variable ordering structures (VOSs). In vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondominated/ minimal solutions are defined in different senses (Henig, Benson, and Borwein) for problems with VOSs from new stand-points. The relationships among the introduced notions are studied, and some scalarization approaches are developed to characterize these solutions. These scalarization results based on new functionals defined by elements from the dual cones are given. Moreover, some existing results are ad-dressed.

کلیدواژه‌ها

Approximate proper solutions؛ Variable ordering structure؛ Scalar-ization؛ Vector optimization

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