Proper efficiency conditions and duality for multiobjective programming problems involving semilocally invex functions

Optimization ◽  
1995 ◽  
Vol 34 (1) ◽  
pp. 43-51 ◽  
Author(s):  
L. N. Das ◽  
S. Nanda
Keyword(s):  
Multiobjective Programming ◽  
Proper Efficiency ◽  
Invex Functions ◽  
Multiobjective Programming Problems ◽  
Efficiency Conditions

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.

scholarly journals Duality of(h,φ)-Multiobjective Programming Involving Generalized Invex Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
GuoLin Yu
Keyword(s):  
Vector Function ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Invex Functions ◽  
Generalized Invex Functions ◽  
Algebraic Operations ◽  
Multiobjective Programming Problems ◽  
Proper Efficient Solution

In the setting of Ben-Tal's generalized algebraic operations, this paper deals with Mond-Weir type dual theorems of multiobjective programming problems involving generalized invex functions. Two classes of functions, namely,(h,φ)-pseudoinvex and(h,φ)-quasi-invex, are defined for a vector function. By utilizing these two classes of functions, some dual theorems are established for conditionally proper efficient solution in(h,φ)-multiobjective programming problems.

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
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