Cone arcwise connectivity in optimization problems with difference of set-valued mappings

Koushik Das; Izhar Ahmad; Savin Treanţă

doi:10.1007/s40324-023-00338-0

Cone arcwise connectivity in optimization problems with difference of set-valued mappings

Koushik Das^*
, Izhar Ahmad
, Savin Treanţă

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

By using ρ cone arcwise connectivity and contingent epi-derivative suppositions, we show the circumstances of sufficiency of the Karush-Kuhn-Tucker type for an optimization problem having the objective mappings and the associated constraints as the difference of set-valued mappings. We also prove the analogous weak, converse, and strong dualities for the Wolfe-type dual of the optimization problem. To back up our findings, we present several instances. Our conclusions reduce to those of optimization problems as the difference of scalar-valued mappings as a particular instance.

Original language	English
Pages (from-to)	511-529
Number of pages	19
Journal	SeMA Journal
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s40324-023-00338-0
State	Published - Sep 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2023.

Keywords

26B25
49N15
Contingent epi-derivative
Convex cone
Duality
Set-valued mapping
ρ cone arcwise connectivity

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Control and Optimization
Applied Mathematics

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Cite this

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abstract = "By using ρ cone arcwise connectivity and contingent epi-derivative suppositions, we show the circumstances of sufficiency of the Karush-Kuhn-Tucker type for an optimization problem having the objective mappings and the associated constraints as the difference of set-valued mappings. We also prove the analogous weak, converse, and strong dualities for the Wolfe-type dual of the optimization problem. To back up our findings, we present several instances. Our conclusions reduce to those of optimization problems as the difference of scalar-valued mappings as a particular instance.",

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T1 - Cone arcwise connectivity in optimization problems with difference of set-valued mappings

AU - Das, Koushik

AU - Ahmad, Izhar

AU - Treanţă, Savin

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2023.

PY - 2024/9

Y1 - 2024/9

N2 - By using ρ cone arcwise connectivity and contingent epi-derivative suppositions, we show the circumstances of sufficiency of the Karush-Kuhn-Tucker type for an optimization problem having the objective mappings and the associated constraints as the difference of set-valued mappings. We also prove the analogous weak, converse, and strong dualities for the Wolfe-type dual of the optimization problem. To back up our findings, we present several instances. Our conclusions reduce to those of optimization problems as the difference of scalar-valued mappings as a particular instance.

AB - By using ρ cone arcwise connectivity and contingent epi-derivative suppositions, we show the circumstances of sufficiency of the Karush-Kuhn-Tucker type for an optimization problem having the objective mappings and the associated constraints as the difference of set-valued mappings. We also prove the analogous weak, converse, and strong dualities for the Wolfe-type dual of the optimization problem. To back up our findings, we present several instances. Our conclusions reduce to those of optimization problems as the difference of scalar-valued mappings as a particular instance.

KW - 26B25

KW - 49N15

KW - Contingent epi-derivative

KW - Convex cone

KW - Duality

KW - Set-valued mapping

KW - ρ cone arcwise connectivity

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DO - 10.1007/s40324-023-00338-0

M3 - Article

AN - SCOPUS:85174505175

SN - 2254-3902

VL - 81

SP - 511

EP - 529

JO - SeMA Journal

JF - SeMA Journal

IS - 3

ER -

Cone arcwise connectivity in optimization problems with difference of set-valued mappings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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