Angewandte Funktionalanalysis

Göpfert, Alfred; Riedrich, Thomas; Tammer, Christiane

doi:10.1007/978-3-8348-9572-1

Cited by 6 publications

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“…We denote by B(y, ε) the open ball with center y ∈ Y and radius ε > 0. See [11,22,23,27] for basic definitions and concepts for vector optimization. Also, see [19,20,34,41] for some scalarization methods for solving vector optimization problems with respect to fixed order structures and some properties of these scalarization methods.…”

Section: Preliminariesmentioning

confidence: 99%

Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Soleimani

Tammer

2014

Vietnam J. Math.

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In this paper, we introduce the concepts for approximately minimal, approximately nondominated solutions, and approximate minimizers of vector optimization problems with respect to variable order structures. In order to describe solution concepts, we use a set-valued map and this map is not necessarily a (pointed, convex) cone-valued map. We illustrate the different concepts for approximate solutions by several examples. Important properties of these three different kinds of approximate solutions of vector optimization problems with respect to variable order structures are discussed. Finally, we give some necessary conditions for approximate solutions of vector optimization problems with variable order structures using a vector-valued variant of Ekeland's variational principle.

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Section: Preliminariesmentioning

confidence: 99%

Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Soleimani

Tammer

2014

Vietnam J. Math.

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“…i.e., the scalarized problem (SP) is an inf-sup problem. Therefore (see [10,Satz 5.19]), it has the dual problem of form: sup…”

Section: 1mentioning

confidence: 99%

Duality in vector optimization with domination structures

2019

Appl. Set-Valued Anal. Optim.

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In this paper, we study duality schemes for vector optimization problems with respect to variable domination structures by using an appropriate extension of the so-called Gerstewitz nonlinear scalarization function for dealing with weakly nondominated solutions. We apply these results to multiobjective location problems with variable domination structures. For nondominated solutions, we use a general scalarization function which is strictly monotone with respect to the domination structure. The strict monotonicity of our proposed function is also discussed.

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Beobachter mit großer Verstärkung und starke Beobachter

Röbenack

2017

Nichtlineare Regelungssysteme

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Angewandte Funktionalanalysis

Cited by 6 publications

References 0 publications

Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Duality in vector optimization with domination structures

Beobachter mit großer Verstärkung und starke Beobachter

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