Generalized α-univexity and duality for nondifferentiable minimax fractional programming

S. K. Mishra; R. P. Pant; J. S. Rautela

doi:10.1016/j.na.2007.11.039

Generalized α-univexity and duality for nondifferentiable minimax fractional programming

S. K. Mishra, R. P. Pant, J. S. Rautela

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

9 Citations (Scopus)

Abstract

The aim of the present paper is to study a nondifferentiable minimax fractional programming problem under the assumptions of α-univex and related functions. In this paper we introduce the concepts of α-univex, pseudo α-univex, strict pseudo α-univex and quasi α-univex functions respectively by unifying the notions of α-invex and univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.

Original language	English
Pages (from-to)	144-158
Number of pages	15
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	1
DOIs	https://doi.org/10.1016/j.na.2007.11.039
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Duality
Generalized convexity
Nondifferentiable minimax fractional programming problems
Sufficient optimality conditions
α-univexity

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2007.11.039

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abstract = "The aim of the present paper is to study a nondifferentiable minimax fractional programming problem under the assumptions of α-univex and related functions. In this paper we introduce the concepts of α-univex, pseudo α-univex, strict pseudo α-univex and quasi α-univex functions respectively by unifying the notions of α-invex and univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.",

keywords = "Duality, Generalized convexity, Nondifferentiable minimax fractional programming problems, Sufficient optimality conditions, α-univexity",

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year = "2009",

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AU - Mishra, S. K.

AU - Pant, R. P.

AU - Rautela, J. S.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - The aim of the present paper is to study a nondifferentiable minimax fractional programming problem under the assumptions of α-univex and related functions. In this paper we introduce the concepts of α-univex, pseudo α-univex, strict pseudo α-univex and quasi α-univex functions respectively by unifying the notions of α-invex and univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.

AB - The aim of the present paper is to study a nondifferentiable minimax fractional programming problem under the assumptions of α-univex and related functions. In this paper we introduce the concepts of α-univex, pseudo α-univex, strict pseudo α-univex and quasi α-univex functions respectively by unifying the notions of α-invex and univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.

KW - Duality

KW - Generalized convexity

KW - Nondifferentiable minimax fractional programming problems

KW - Sufficient optimality conditions

KW - α-univexity

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DO - 10.1016/j.na.2007.11.039

M3 - Article

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SN - 0362-546X

VL - 70

SP - 144

EP - 158

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1

ER -

Generalized α-univexity and duality for nondifferentiable minimax fractional programming

Abstract

Keywords

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