Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces

2012 ◽  
Vol 156 (3) ◽  
pp. 683-700 ◽  
Author(s):  
Luis Rodríguez-Marín ◽  
Miguel Sama
Keyword(s):  
Lagrange Multiplier ◽  
Infinite Dimensional ◽  
Multiplier Rules

scholarly journals Quasi-regularity in Optimization

1986 ◽  
Vol 41 (2) ◽  
pp. 188-192 ◽  
Author(s):  
Kung-Fu Ng ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
General Situation ◽  
Lagrange Multiplier Rule ◽  
Infinite Dimensional ◽  
Space Setting ◽  
Multiplier Rule ◽  
Dimensional Version ◽  
Definition Of

AbstractThe notion of quasi-regularity, defined for optimization problems in Rn, is extended to the Banach space setting. Examples are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.

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.

scholarly journals Sensitivity functionals in convex optimization problem

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3681-3687
Author(s):  
Robert Namm ◽  
Gyungsoo Woo
Keyword(s):  
Variational Inequality ◽  
Convex Optimization ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Convex Optimization Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional

We consider sensitivity functionals and Lagrange multiplier method for solving finite dimensional convex optimization problem.An analysis based on this property is also applied for semicoercive infinite dimensional variational inequality in mechanics.

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.

Sign in / Sign up

Export Citation Format

Share Document