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Optim Lett (2008) 2:599604 DOI 10.1007/s11590-008-0075-8

Summary: Optim Lett (2008) 2:599­604
DOI 10.1007/s11590-008-0075-8
Note on Mond­Weir type nondifferentiable
second order symmetric duality
Z. Husain · I. Ahmad
Received: 20 July 2007 / Accepted: 11 January 2008 / Published online: 29 January 2008
© Springer-Verlag 2008
Abstract In this paper, we point out some inconsistencies in the earlier work of
Ahmad and Husain (Appl. Math. Lett. 18, 721­728, 2005), and present the correct
forms of their strong and converse duality theorems.
Keywords Nondifferentiable programming · Multiobjective programming ·
Second order symmetric duality
1 Introduction
In connection with symmetric duality in multiobjective programming, Ahmad and
Husain [1] formulated a pair of Mond­Weir type nondifferentiable multiobjective
second order symmetric dual programs and established weak, strong and converse
duality theorems under second order F-pseudoconvexity/F-pseudoconcavity assum-
pions. But, in their strong duality theorem, the assumptions made by them are seemed
to be incorrect.


Source: Ahmad, Izahr - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics