Generalized α-invexity and nondifferentiable minimax fractional programming

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

doi:10.1016/j.cam.2006.06.009

Generalized α-invexity and nondifferentiable minimax fractional programming

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

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

Abstract

In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of α-invex function. In this paper we utilize the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo-α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75]. We also introduce the concept of strict pseudo-α-invex and quasi-α-invex 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. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	122-135
Journal	Journal of Computational and Applied Mathematics
Volume	206
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2006.06.009
Publication status	Published - 1 Sept 2007

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

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

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title = "Generalized α-invexity and nondifferentiable minimax fractional programming",

abstract = "In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of α-invex function. In this paper we utilize the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo-α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75]. We also introduce the concept of strict pseudo-α-invex and quasi-α-invex 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. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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

author = "Mishra, \{S. K.\} and Pant, \{R. P.\} and Rautela, \{J. S.\}",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

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AU - Mishra, S. K.

AU - Pant, R. P.

AU - Rautela, J. S.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2007/9/1

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N2 - In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of α-invex function. In this paper we utilize the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo-α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75]. We also introduce the concept of strict pseudo-α-invex and quasi-α-invex 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. © 2006 Elsevier B.V. All rights reserved.

AB - In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of α-invex function. In this paper we utilize the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo-α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75]. We also introduce the concept of strict pseudo-α-invex and quasi-α-invex 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. © 2006 Elsevier B.V. All rights reserved.

KW - α-invexity

KW - Duality

KW - Generalized convexity

KW - Nondifferentiable minimax fractional programming problems

KW - Sufficient optimality conditions

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U2 - 10.1016/j.cam.2006.06.009

DO - 10.1016/j.cam.2006.06.009

M3 - RGC 21 - Publication in refereed journal

SN - 0377-0427

VL - 206

SP - 122

EP - 135

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Generalized α-invexity and nondifferentiable minimax fractional programming

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