Henig proper efficiency in vector optimization with variable ordering structure

Marius Durea; Elena-Andreea Florea; Radu Strugariu

doi:10.3934/jimo.2018071

Article Contents

2019, Volume 15, Issue 2: 791-815. Doi: 10.3934/jimo.2018071

This issue Previous Article Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors Next Article On the global optimal solution for linear quadratic problems of switched system

Henig proper efficiency in vector optimization with variable ordering structure

1.
Faculty of Mathematics, "Alexandru Ioan Cuza" University, Bd. Carol Ⅰ, nr. 11, Iaşi, 700506, Romania
2.
"Octav Mayer" Institute of Mathematics of the Romanian Academy, Bd. Carol Ⅰ, nr. 8, Iaşi, 700505, Romania
3.
Department of Mathematics, "Gh. Asachi" Technical University, Bd. Carol Ⅰ, nr. 11, Iaşi, 700506, Romania

* Corresponding author: Marius Durea
* Corresponding author: Marius Durea

Received: October 2016

Revised: March 2018

Early access: June 2018

Published: January 2019

The work of the authors was supported by a grant of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-Ⅲ-P4-ID-PCE-2016-0188, within PNCDI Ⅲ.

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Abstract

In this paper we introduce a notion of Henig proper efficiency for constrained vector optimization problems in the setting of variable ordering structure. In order to get an appropriate concept, we have to explore firstly the case of fixed ordering structure and to observe that, in certain situations, the well-known Henig proper efficiency can be expressed in a simpler way. Then, we observe that the newly introduced notion can be reduced, by a Clarke-type penalization result, to the notion of unconstrained robust efficiency. We show that this penalization technique, coupled with sufficient conditions for weak openness, serves as a basis for developing necessary optimality conditions for our Henig proper efficiency in terms of generalized differentiation objects lying in both primal and dual spaces.

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Mathematics Subject Classification: Primary: 90C30; Secondary: 90C31, 49K40.

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