Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints

Rekha R. Jaichander; Izhar Ahmad; Krishna Kummari; Suliman Al-Homidan

doi:10.3390/math10111787

Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints

Rekha R. Jaichander, Izhar Ahmad^*, Krishna Kummari, Suliman Al-Homidan

^*Corresponding author for this work

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

1 Scopus citations

Abstract

In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LUoptimal solution and the generalized robust Slater constraint qualification (GRSCQ). These KarushKuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples.

Original language	English
Article number	1787
Journal	Mathematics
Volume	10
Issue number	11
DOIs	https://doi.org/10.3390/math10111787
State	Published - 1 Jun 2022

Bibliographical note

Funding Information:
Acknowledgments: The second and fourth authors would like to thank the King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia to provide the financial support. Also, the authors would like to express their gratitude to the anonymous referees for their insightful recommendations and comments, which dramatically improved this manuscript to its present state.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Generalized convexity
LUoptimal solution
duality
optimality
robust nonsmooth interval-valued optimization problem

ASJC Scopus subject areas

Computer Science (miscellaneous)
Engineering (miscellaneous)
Mathematics (all)

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10.3390/math10111787

Cite this

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title = "Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints",

abstract = "In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LUoptimal solution and the generalized robust Slater constraint qualification (GRSCQ). These KarushKuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples.",

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AU - Kummari, Krishna

AU - Al-Homidan, Suliman

N1 - Funding Information: Acknowledgments: The second and fourth authors would like to thank the King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia to provide the financial support. Also, the authors would like to express their gratitude to the anonymous referees for their insightful recommendations and comments, which dramatically improved this manuscript to its present state. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/6/1

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N2 - In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LUoptimal solution and the generalized robust Slater constraint qualification (GRSCQ). These KarushKuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples.

AB - In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a robust nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LUoptimal solution and the generalized robust Slater constraint qualification (GRSCQ). These KarushKuhn-Tucker type robust necessary conditions are shown to be sufficient optimality conditions under generalized convexity. The Wolfe and Mond-Weir type robust dual problems are formulated over cones using generalized convexity assumptions, and usual duality results are established. The presented results are illustrated by non-trivial examples.

KW - Generalized convexity

KW - LUoptimal solution

KW - duality

KW - optimality

KW - robust nonsmooth interval-valued optimization problem

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ER -

Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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