Optimality Criteria and Duality in Multiobjective Programming Involving Nonsmooth Invex Functions

2006 ◽  
Vol 35 (4) ◽  
pp. 593-606 ◽  
Author(s):  
S. Nobakhtian
Keyword(s):  
Multiobjective Programming ◽  
Optimality Criteria ◽  
Invex Functions

Invex Functions and Generalized Convexity in Multiobjective Programming

1998 ◽  
Vol 98 (3) ◽  
pp. 651-661 ◽  
Author(s):  
R. Osuna-Gómez ◽  
A. Rufián-Lizana ◽  
P. Ruíz-Canales
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Invex Functions

scholarly journals On semi-G-V-type I concepts for directionally differentiable multiobjective programming problems

2016 ◽  
Vol 6 (2) ◽  
pp. 189-203
Author(s):  
Tadeusz Antczak ◽  
Gabriel Ruiz-Garzón
Keyword(s):  
Optimality Conditions ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Invex Functions ◽  
Differentiable Functions ◽  
Necessary And Sufficient ◽  
Multiobjective Programming Problems

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs.

Sign in / Sign up

Export Citation Format

Share Document