Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Izhar Ahmad; Arshpreet Kaur; Mahesh Kumar Sharma

doi:10.1051/ro/2021095

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Izhar Ahmad, Arshpreet Kaur^*, Mahesh Kumar Sharma

^*Corresponding author for this work

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

1 Scopus citations

Abstract

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

Original language	English
Pages (from-to)	2181-2188
Number of pages	8
Journal	RAIRO - Operations Research
Volume	55
Issue number	4
DOIs	https://doi.org/10.1051/ro/2021095
State	Published - 1 Jul 2021

Bibliographical note

Funding Information:
Acknowledgements. The first author thanks the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for the support under the Small/Basic Research grant No. SB191005. The authors wish to thank the referees for their valuable suggestions which have considerably improved the presentation of the paper.

Publisher Copyright:
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021.

Keywords

Generalized convexity
Robust duality
Robust nonsmooth optimization

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Management Science and Operations Research

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10.1051/ro/2021095

Cite this

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title = "Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints",

abstract = "Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.",

keywords = "Generalized convexity, Robust duality, Robust nonsmooth optimization",

author = "Izhar Ahmad and Arshpreet Kaur and Sharma, {Mahesh Kumar}",

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AU - Ahmad, Izhar

AU - Kaur, Arshpreet

AU - Sharma, Mahesh Kumar

N1 - Funding Information: Acknowledgements. The first author thanks the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for the support under the Small/Basic Research grant No. SB191005. The authors wish to thank the referees for their valuable suggestions which have considerably improved the presentation of the paper. Publisher Copyright: © The authors. Published by EDP Sciences, ROADEF, SMAI 2021.

PY - 2021/7/1

Y1 - 2021/7/1

N2 - Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

AB - Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

KW - Generalized convexity

KW - Robust duality

KW - Robust nonsmooth optimization

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DO - 10.1051/ro/2021095

M3 - Article

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VL - 55

SP - 2181

EP - 2188

JO - RAIRO - Operations Research

JF - RAIRO - Operations Research

IS - 4

ER -

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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