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Journal of Applied Analysis Vol. 14, No. 1 (2008), pp. 131-148
 

Summary: Journal of Applied Analysis
Vol. 14, No. 1 (2008), pp. 131-148
SECOND ORDER DUALITY IN
MULTIOBJECTIVE PROGRAMMING
I. AHMAD and Z. HUSAIN
Received November 10, 2006 and, in revised form, November 6, 2007
Abstract. A nonlinear multiobjective programming problem is consid-
ered. Weak, strong and strict converse duality theorems are established
under generalized second order (F, , , d)-convexity for second order
Mangasarian type and general Mond-Weir type vector duals.
1. Introduction
In recent years, there has been an increasing interest in generalizations of
convexity in connection with sufficiency and duality in optimization prob-
lems. It has been found that only a few properties of convex functions are
needed for establishing sufficiency and duality theorems. Using properties
needed as definitions of new classes of functions, it is possible to generalize
the notion of convexity and to extend the validity of theorems to larger
classes of optimization problems. Consequently, several classes of gener-
alized convexity have been introduced. More specifically, the concept of
2000 Mathematics Subject Classification. Primary: 90C29, 90C30, 90C46.

  

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

 

Collections: Mathematics