scholarly journals First-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis

2011 ◽  
Vol 21 (4) ◽  
pp. 1561-1593 ◽  
Author(s):  
M. Hintermüller ◽  
T. Surowiec
Keyword(s):  
Optimality Conditions ◽  
Variational Analysis ◽  
Equilibrium Constraints ◽  
First Order ◽  
Mathematical Programs ◽  
First Order Optimality Conditions

Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints

2019 ◽  
Vol 53 (5) ◽  
pp. 1617-1632 ◽  
Author(s):  
Bhawna Kohli
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Mathematical Programs ◽  
Strong Stationarity ◽  
Necessary And Sufficient

The main aim of this paper is to develop necessary Optimality conditions using Convexifactors for mathematical programs with equilibrium constraints (MPEC). For this purpose a nonsmooth version of the standard Guignard constraint qualification (GCQ) and strong stationarity are introduced in terms of convexifactors for MPEC. It is shown that Strong stationarity is the first order necessary optimality condition under nonsmooth version of the standard GCQ. Finally, notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are used to establish the sufficient optimality conditions for MPEC.

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.

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