On Several Types of Basic Constraint Qualifications via Coderivatives for Generalized Equations
In this paper, we study several types of basic constraint qualifications in terms of Clarke/Fréchet coderivatives for generalized equations. Several necessary and/or sufficient conditions are given to ensure these constraint qualifications. It is proved that basic constraint qualification and strong...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 177; H. 1; S. 106 - 126 |
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| Sprache: | Englisch |
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| Abstract | In this paper, we study several types of basic constraint qualifications in terms of Clarke/Fréchet coderivatives for generalized equations. Several necessary and/or sufficient conditions are given to ensure these constraint qualifications. It is proved that basic constraint qualification and strong basic constraint qualification for convex generalized equations can be obtained by these constraint qualifications, and the existing results on constraint qualifications for the inequality system can be deduced from the given conditions in this paper. The main work of this paper is an extension of the study on constraint qualifications from inequality systems to generalized equations. |
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| AbstractList | In this paper, we study several types of basic constraint qualifications in terms of Clarke/Fréchet coderivatives for generalized equations. Several necessary and/or sufficient conditions are given to ensure these constraint qualifications. It is proved that basic constraint qualification and strong basic constraint qualification for convex generalized equations can be obtained by these constraint qualifications, and the existing results on constraint qualifications for the inequality system can be deduced from the given conditions in this paper. The main work of this paper is an extension of the study on constraint qualifications from inequality systems to generalized equations. |
| Author | Yao, Jen-Chih Wei, Zhou |
| Author_xml | – sequence: 1 givenname: Zhou surname: Wei fullname: Wei, Zhou organization: Department of Mathematics, Yunnan University – sequence: 2 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih email: yaojc@mail.cmu.edu.tw organization: Center for General Education, China Medical University, Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University |
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| Cites_doi | 10.1007/s11228-008-0076-x 10.1137/S1052623495287927 10.1137/080714129 10.1023/B:SVAN.0000023394.19482.30 10.1007/978-1-4612-5200-9 10.1070/RM2000v055n03ABEH000292 10.1137/060676982 10.1287/moor.1050.0154 10.1016/S0362-546X(98)00031-5 10.1007/s10107-005-0614-3 10.1137/S1052623403423102 10.1137/080739124 10.1007/978-3-662-21569-2 10.1080/02331939008843516 10.1090/S0002-9947-1972-0313769-9 10.1016/j.na.2007.05.021 10.1137/07068432X 10.1016/0362-546X(89)90083-7 10.1007/s10107-013-0641-4 10.1002/mana.200510662 10.1090/S0002-9947-1993-1156300-4 10.1137/050648079 10.1007/s10107-005-0623-2 10.1137/S1052623402415846 10.1137/050644872 10.1007/s11590-017-1172-3 |
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| Keywords | 90C31 Normal cone 90C25 49J52 Coderivative Generalized equation 46B20 End set Basic constraint qualification |
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| Snippet | In this paper, we study several types of basic constraint qualifications in terms of Clarke/Fréchet coderivatives for generalized equations. Several necessary... |
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| SubjectTerms | Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Engineering Mathematical analysis Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Qualifications Theory of Computation |
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| Title | On Several Types of Basic Constraint Qualifications via Coderivatives for Generalized Equations |
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