On the multiplier rules

Optimization ◽  
2015 ◽  
Vol 65 (5) ◽  
pp. 947-955 ◽  
Author(s):  
Joël Blot
Keyword(s):  
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

Multiplier rules for weak pareto optimization problems

Optimization ◽  
1996 ◽  
Vol 38 (1) ◽  
pp. 23-37 ◽  
Author(s):  
W. W. Breckner ◽  
A. Göpfert
Keyword(s):  
Optimization Problems ◽  
Pareto Optimization ◽  
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.

Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950021
Author(s):  
Tijani Amahroq ◽  
Abdessamad Oussarhan
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multiplier ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Set Optimization ◽  
Vector Equilibrium Problems ◽  
Multiplier Rules ◽  
Convexity Assumption ◽  
Vector Equilibrium ◽  
Weak Vector

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.

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