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On vectorization strategies in set optimization

delete2026-01-01
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PRE
AI
G
Gabriele Eichfelder *
T
Tobias Gerlach
DOI:10.1007/s00186-025-00912-4delete
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Abstract

Abstract

En 中文
In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect and discuss the most important properties and relationships between the approaches.
Keywords:
Set optimization
Set approach
Multi-objective optimization
Vectorization

Journal

M
Mathematical Methods of Operations Research
IF:
1.2
Papers:
24
Citations:
0

Organization

T
Technische Universitat Ilmenau
Scholars:
2.4K
Papers: 2.0K
Citations: 20
Cited Papers

Cited Papers

A vectorization for nonconvex set-valued optimization
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PREAI
errKARAMAN,Emrah; ATASEVER GÜVENÇ,İlknur; SOYERTEM,Mustafa; TOZKAN,Didem; KÜÇÜK,Mahide; KÜÇÜK,Yalçın
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The relationship between multi-objective robustness concepts and set-valued optimization
err2014-03-31
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errOAAI
errJonas Ide; Elisabeth Köbis; Daishi Kuroiwa; Anita Schöbel; Christiane Tammer
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Some useful set-valued maps in set optimization
err2017-08-03
err0
PREAI
errHernández,Elvira; López,Rubén
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A Vectorization Scheme for Nonconvex Set Optimization Problems
err2022-05-31
err0
errOAAI
errGabriele Eichfelder; Ernest Quintana; Stefan Rocktäschel
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