Sufficiency and duality in interval-valued variational programming

I. Ahmad; Anurag Jayswal; S. Al-Homidan; Jonaki Banerjee

doi:10.1007/s00521-017-3307-y

Sufficiency and duality in interval-valued variational programming

I. Ahmad^*, Anurag Jayswal, S. Al-Homidan, Jonaki Banerjee

^*Corresponding author for this work

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

18 Scopus citations

Abstract

In the present paper, we focus our study on an interval-valued variational problem and derive sufficient optimality conditions by using the notion of invexity. In order to relate the primal interval-valued variational problem and its dual, several duality results, viz., weak, strong and converse duality results are established. Further, the Lagrangian function for the considered interval-valued variational problem is defined and we present some relations between an optimal solution of the considered interval-valued variational problem and a saddle point of the Lagrangian function. In order to illustrate the results proved in the paper, some examples of interval-valued variational problems have been formulated.

Original language	English
Pages (from-to)	4423-4433
Number of pages	11
Journal	Neural Computing and Applications
Volume	31
Issue number	8
DOIs	https://doi.org/10.1007/s00521-017-3307-y
State	Published - 1 Aug 2019

Bibliographical note

Funding Information:
The research of the first and third author is financially supported by King Fahd University of Petroleum and Minerals, Saudi Arabia under the Internal Research Project No. IN131026.

Publisher Copyright:
© 2018, The Natural Computing Applications Forum.

Keywords

Duality
Interval-valued problem
Invexity
LU optimal
Sufficiency

ASJC Scopus subject areas

Software
Artificial Intelligence

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10.1007/s00521-017-3307-y

Cite this

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AU - Ahmad, I.

AU - Jayswal, Anurag

AU - Al-Homidan, S.

AU - Banerjee, Jonaki

N1 - Funding Information: The research of the first and third author is financially supported by King Fahd University of Petroleum and Minerals, Saudi Arabia under the Internal Research Project No. IN131026. Publisher Copyright: © 2018, The Natural Computing Applications Forum.

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N2 - In the present paper, we focus our study on an interval-valued variational problem and derive sufficient optimality conditions by using the notion of invexity. In order to relate the primal interval-valued variational problem and its dual, several duality results, viz., weak, strong and converse duality results are established. Further, the Lagrangian function for the considered interval-valued variational problem is defined and we present some relations between an optimal solution of the considered interval-valued variational problem and a saddle point of the Lagrangian function. In order to illustrate the results proved in the paper, some examples of interval-valued variational problems have been formulated.

AB - In the present paper, we focus our study on an interval-valued variational problem and derive sufficient optimality conditions by using the notion of invexity. In order to relate the primal interval-valued variational problem and its dual, several duality results, viz., weak, strong and converse duality results are established. Further, the Lagrangian function for the considered interval-valued variational problem is defined and we present some relations between an optimal solution of the considered interval-valued variational problem and a saddle point of the Lagrangian function. In order to illustrate the results proved in the paper, some examples of interval-valued variational problems have been formulated.

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Sufficiency and duality in interval-valued variational programming

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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