Summary: J Optim Theory Appl (2007) 135: 411427
Sufficiency and Duality in Multiobjective Programming
under Generalized Type I Functions
T.R. Gulati · I. Ahmad · D. Agarwal
Published online: 25 August 2007
© Springer Science+Business Media, LLC 2007
Abstract In this paper, new classes of generalized (F,,,d)-V -type I functions
are introduced for differentiable multiobjective programming problems. Based upon
these generalized convex functions, sufficient optimality conditions are established.
Weak, strong and strict converse duality theorems are also derived for Wolfe and
Mond-Weir type multiobjective dual programs.
Keywords Multiobjective programming · Generalized type I functions · Weak
Efficiency · Sufficiency · Duality
In 1981, Hanson  introduced the concept of invexity and established Karush-Kuhn-
Tucker type sufficient optimality conditions for a nonlinear programming problem.
Later, Hanson and Mond  defined two new classes of functions, called type I
and type II functions in nonlinear programming, which were further generalized to
pseudo-type I and quasi-type I functions by Rueda and Hanson . Both classes are