Optimality Conditions for Cardinality Constrained Optimization Problems

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dc.contributor.authorXiao, Zhuoyu
dc.contributor.supervisorYe, Juan Juan
dc.date.accessioned2022-08-11T16:30:30Z
dc.date.available2022-08-11T16:30:30Z
dc.date.copyright2022en_US
dc.date.issued2022-08-11
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractCardinality constrained optimization problems (CCOP) are a new class of optimization problems with many applications. In this thesis, we propose a framework called mathematical programs with disjunctive subspaces constraints (MPDSC), a special case of mathematical programs with disjunctive constraints (MPDC), to investigate CCOP. Our method is different from the relaxed complementarity-type reformulation in the literature. The first contribution of this thesis is that we study various stationarity conditions for MPDSC, and then apply them to CCOP. In particular, we recover disjunctive-type strong (S-) stationarity and Mordukhovich (M-) stationarity for CCOP, and then reveal the relationship between them and those from the relaxed complementarity-type reformulation. The second contribution of this thesis is that we obtain some new results for MPDSC, which do not hold for MPDC in general. We show that many constraint qualifications like the relaxed constant positive linear dependence (RCPLD) coincide with their piecewise versions for MPDSC. Based on such result, we prove that RCPLD implies error bounds for MPDSC. These two results also hold for CCOP. All of these disjunctive-type constraint qualifications for CCOP derived from MPDSC are weaker than those from the relaxed complementarity-type reformulation in some sense.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/14091
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectcardinality constrained optimization problemsen_US
dc.subjectdisjunctive subspaces constraintsen_US
dc.subjectnecessary optimality conditionsen_US
dc.subjectconstraint qualificationsen_US
dc.subjectmetric subregularityen_US
dc.subjecterror bounds propertyen_US
dc.titleOptimality Conditions for Cardinality Constrained Optimization Problemsen_US
dc.typeThesisen_US

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