Summary: Second order (F,a,q,d)-convexity and
duality in multiobjective programming
I. Ahmad, Z. Husain *
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
Received 24 November 2004; received in revised form 10 August 2005; accepted 12 August 2005
A class of second order (F,a,q,d)-convex functions and their generalizations is intro-
duced. Using the assumptions on the functions involved, weak, strong and strict
converse duality theorems are established for a second order Mond≠Weir type multi-
” 2005 Elsevier Inc. All rights reserved.
Keywords: Multiobjective programming; Second order duality; Efficient solutions; Generalized
The importance of convex functions is well known in optimization theory.
But for many mathematical models used in decision sciences, economics, man-
agement sciences, stochastics, applied mathematics and engineering, the notion
0020-0255/$ - see front matter ” 2005 Elsevier Inc. All rights reserved.