scholarly journals Lagrange multiplier rules for approximate solutions in vector optimization

2012 ◽  
Vol 8 (3) ◽  
pp. 749-764 ◽  
Author(s):  
Caiping Liu ◽  
Heungwing Lee
Keyword(s):  
Vector Optimization ◽  
Lagrange Multiplier ◽  
Approximate Solutions ◽  
Multiplier Rules

Multiplier Rules and Saddle-Point Theorems for Helbig’s Approximate Solutions in Convex Pareto Problems

2005 ◽  
Vol 32 (3) ◽  
pp. 367-383 ◽  
Author(s):  
César Gutiérrez ◽  
Bienvenido Jiménez ◽  
Vicente Novo
Keyword(s):  
Saddle Point ◽  
Approximate Solutions ◽  
Multiplier Rules

SEQUENTIAL LAGRANGE MULTIPLIER CONDITIONS FOR MINIMAX PROGRAMMING PROBLEMS

2008 ◽  
Vol 25 (02) ◽  
pp. 113-133 ◽  
Author(s):  
ANULEKHA DHARA ◽  
APARNA MEHRA
Keyword(s):  
Lagrange Multiplier ◽  
Constraint Qualification ◽  
Minimax Programming ◽  
Duality Results ◽  
Multiplier Rules ◽  
Cone Constraint

In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ∊-subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.

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