Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization

2014 ◽  
pp. 133-153
Author(s):  
Michael Hintermüller ◽  
Antoine Laurain ◽  
Caroline Löbhard ◽  
Carlos N. Rautenberg ◽  
Thomas M. Surowiec
Keyword(s):  
Optimality Conditions ◽  
Function Space ◽  
Numerical Realization ◽  
Equilibrium Constraints ◽  
Mathematical Programs

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.

Optimality conditions for nonsmooth mathematical programs with equilibrium constraints, using convexificators

Optimization ◽  
2014 ◽  
Vol 65 (1) ◽  
pp. 67-85 ◽  
Author(s):  
A. Ansari Ardali ◽  
N. Movahedian ◽  
S. Nobakhtian
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs

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.

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