Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria

Anurag Jayswal; I. Ahmad; Jonaki Banerjee

doi:10.1007/s40840-015-0237-7

Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria

Anurag Jayswal^*, I. Ahmad, Jonaki Banerjee

^*Corresponding author for this work

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

17 Scopus citations

Abstract

In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be an LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point-type optimality conditions are established in order to find relation between LU optimal solution of primal and saddle point of Lagrangian function.

Original language	English
Pages (from-to)	1391-1411
Number of pages	21
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	39
Issue number	4
DOIs	https://doi.org/10.1007/s40840-015-0237-7
State	Published - 1 Oct 2016

Bibliographical note

Funding Information:
The research of the first author was partially supported by DST, New Delhi, India, through Grant no. SR/FTP/MS-007/2011. The authors wish to thank the referees for their valuable suggestions which improved the presentation of the paper.

Publisher Copyright:
© 2015, Malaysian Mathematical Sciences Society and Universiti Sains Malaysia.

Keywords

Duality
Interval-valued programming
Invexity
LU optimal
Lagrangian function
Sufficiency

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s40840-015-0237-7

Cite this

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title = "Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria",

abstract = "In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be an LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point-type optimality conditions are established in order to find relation between LU optimal solution of primal and saddle point of Lagrangian function.",

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N2 - In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be an LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point-type optimality conditions are established in order to find relation between LU optimal solution of primal and saddle point of Lagrangian function.

AB - In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be an LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point-type optimality conditions are established in order to find relation between LU optimal solution of primal and saddle point of Lagrangian function.

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Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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