scholarly journals Saddle points criteria in nondifferentiable multiobjective programming with V-invex functions via an η-approximation method

2010 ◽  
Vol 60 (9) ◽  
pp. 2689-2700 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Approximation Method ◽  
Multiobjective Programming ◽  
Saddle Points ◽  
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 Saddle point criteria and duality in multiobjective programming via an η-approximation method

2005 ◽  
Vol 47 (2) ◽  
pp. 155-172 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Programming Problem ◽  
Dual Problem ◽  
Multiobjective Programming ◽  
Lagrange Function ◽  
Saddle Points ◽  
Duality Theorems ◽  
Approximation Approach ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems

AbstractIn this paper, Antczak's η-approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the η-saddle points of the associated η-approximated vector optimisation problems. We introduce an η-Lagrange function for a constructed η-approximated vector optimisation problem and present some modified η-saddle point results. Furthermore, we construct an η-approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between η-approximation vector optimisation problems and their duals (that is, an η-approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.

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