Bounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraints

2016 ◽  
Vol 67 (4) ◽  
pp. 829-850 ◽  
Author(s):  
Nooshin Movahedian
Keyword(s):  
Lagrange Multiplier ◽  
Equilibrium Constraints ◽  
Multiplier Rules ◽  
Mathematical Programs ◽  
Nonsmooth Problems

scholarly journals A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

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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