On properly nondominated solutions in vector optimization with a variable ordering structure

سال انتشار: 1398
نوع سند: مقاله کنفرانسی
زبان: انگلیسی
مشاهده: 315

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ICIORS12_108

تاریخ نمایه سازی: 24 شهریور 1398

چکیده مقاله:

In Vector Optimization (VO) with a Variable Ordering Structure (VOS), the partial ordering cone depends on the elements of the image set. A candidate element is said to be nondominated iff it is not dominated by other reference elements w.r.t. their corresponding ordering.In addition to nondominated elements, another notion of optimal elements, called minimality, has also been discussed. For that notion, only the ordering of the candidate element itself is considered. One of the most important notions in VO is properly optimal solutions.In the present work, we introduce and investigate some new properly optimal solutions for VO with a VOS. In additionto characterizing these solution concepts, we establish the connections between different proper efficiency notions, including Hartley, Benson, and super optimal solutions. A considerable part of this presentation will be based on a recent work by Shahbeyk, Soleimani-damaneh, and Kasimbeyli. Since the results concerning minimal points are similar to those related to efficient points with a constant ordering structure, in this paper we focus only on nondominated points.

نویسندگان

Shokouh Shahbeyk

Jamshid Kashani University, Abyek, Qazvin, Iran

Majid Soleimani-damaneh

School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran