Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure

Shokouh Shahbeyk (), Majid Soleimani-damaneh () and Refail Kasimbeyli ()
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Shokouh Shahbeyk: University of Tehran
Majid Soleimani-damaneh: University of Tehran
Refail Kasimbeyli: Anadolu University

Journal of Global Optimization, 2018, vol. 71, issue 2, No 6, 383-405

Abstract: Abstract In this paper, we introduce Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure. We prove the connections between Benson properly nondominated, Hartley properly nondominated, and super nondominated solutions under appropriate assumptions. Moreover, we establish some necessary and sufficient conditions for newly-defined solutions invoking an augmented dual cone approach, the linear scalarization, and variational analysis tools. In addition to the theoretical results, various clarifying examples are given.

Keywords: Vector optimization; Variable ordering structure (VOS); Properly nondominated solution; Super nondominated solution; Augmented dual cone; Linear scalarization; Variational analysis (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-018-0614-5

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