Exact penalty functions and calmness for mathematical programming under nonlinear perturbations

In the present paper, the effects of nonlinear perturbations of constraint systems are considered over the relationship between calmness and exact penalization, within the context of mathematical programming with equilibrium constraints. Two counterexamples are provided showing that the crucial link...

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Veröffentlicht in:Nonlinear analysis Jg. 73; H. 6; S. 1596 - 1609
1. Verfasser: Uderzo, A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Ltd 15.09.2010
Elsevier
Schlagworte:
Calculus of variations and optimal control
Calmness
Exact sciences and technology
Links
Mathematical analysis
Mathematical programming
Mathematics
Metric subregularity
MPEC
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Optimization
Outer Lipschitz continuity
Penalty function
Perturbation methods
Sciences and techniques of general use
Value function
secondary
Penalty function
Metric subregularity
Value function
Outer Lipschitz continuity
MPEC
Calmness
primary
secondary 49J53
Nonlinear analysis
Non linear programming
90C48
Mathematical function
90C31
49M30
primary 90C30
Mathematical model
49K27
Mathematical programming
ISSN:0362-546X, 1873-5215
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Beschreibung
Zusammenfassung:In the present paper, the effects of nonlinear perturbations of constraint systems are considered over the relationship between calmness and exact penalization, within the context of mathematical programming with equilibrium constraints. Two counterexamples are provided showing that the crucial link between the existence of penalty functions and the property of calmness for perturbed problems is broken in the presence of general perturbations. Then, some properties from variational analysis are singled out, which are able to restore to a certain extent the broken link. Consequently, conditions on the value function associated to perturbed optimization problems are investigated in order to guarantee the occurrence of the above properties.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.04.066