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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| Vydané v: | Nonlinear analysis Ročník 73; číslo 6; s. 1596 - 1609 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Amsterdam
Elsevier Ltd
15.09.2010
Elsevier |
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| ISSN: | 0362-546X, 1873-5215 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Uderzo, A. |
| Author_xml | – sequence: 1 givenname: A. surname: Uderzo fullname: Uderzo, A. email: amos.uderzo@unimib.it organization: Department of Statistics, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8-20126 Milan, Italy |
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| CitedBy_id | crossref_primary_10_1007_s11067_012_9178_y crossref_primary_10_1080_02331934_2017_1349125 crossref_primary_10_1007_s11590_015_0886_3 crossref_primary_10_1007_s10957_013_0338_0 crossref_primary_10_1080_02331934_2015_1122005 crossref_primary_10_1007_s10957_013_0288_6 crossref_primary_10_1080_02331934_2014_938074 crossref_primary_10_1080_01630563_2015_1070864 crossref_primary_10_1007_s10013_014_0077_z crossref_primary_10_1007_s10898_012_9900_9 crossref_primary_10_1007_s10898_015_0271_x crossref_primary_10_1134_S008154381901005X |
| Cites_doi | 10.1007/s11228-008-0076-x 10.1287/moor.1.2.165 10.1007/s11228-006-0024-6 10.1137/050648079 10.1080/10556789808805684 10.1016/j.na.2009.01.217 10.1070/RM2000v055n03ABEH000292 10.1007/s10107-005-0623-2 10.1007/BFb0120929 10.1007/s10589-006-6441-5 10.1080/02331930802355390 10.1007/s10107-004-0539-2 10.1023/A:1023296417861 10.1080/10556780310001622229 10.1007/BFb0120850 10.1023/A:1026599021286 10.1007/s11228-007-0047-7 10.1007/s11228-009-0121-4 10.1016/S0362-546X(01)00129-8 10.1137/S0363012996306121 10.1287/mnsc.13.5.344 10.1023/A:1024787424532 10.1137/0317042 10.1080/0233193031000149894 10.1137/0317019 10.1016/0167-6377(88)90066-1 10.1007/BF02592205 10.1023/B:AURC.0000014725.30533.c3 10.1137/0329027 10.1137/0329054 |
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| Issue | 6 |
| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Exact penalty functions and calmness for mathematical programming under nonlinear perturbations |
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