Tangential extremal principles for finite and infinite systems of sets II: applications to semi-infinite and multiobjective optimization
This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011 ) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective...
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| Published in: | Mathematical programming Vol. 136; no. 1; pp. 31 - 63 |
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| Main Authors: | , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
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Berlin/Heidelberg
Springer-Verlag
01.12.2012
Springer Springer Nature B.V |
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| ISSN: | 0025-5610, 1436-4646 |
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| Abstract | This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program
2011
) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints. |
|---|---|
| AbstractList | This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints. Issue Title: Special Issue on Parametric Optimization - Recent Advances This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.[PUBLICATION ABSTRACT] This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011 ) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints. |
| Author | Mordukhovich, Boris S. Phan, Hung M. |
| Author_xml | – sequence: 1 givenname: Boris S. surname: Mordukhovich fullname: Mordukhovich, Boris S. email: boris@math.wayne.edu organization: Department of Mathematics, Wayne State University – sequence: 2 givenname: Hung M. surname: Phan fullname: Phan, Hung M. organization: Department of Mathematics, Wayne State University |
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| Cites_doi | 10.1137/09076595X 10.1137/060652087 10.1137/090765948 10.1007/s101070050083 10.1007/s10107-005-0596-1 10.1016/j.na.2010.04.020 10.1137/060658047 10.1007/BF02564714 10.1007/s10107-008-0249-2 10.1137/S1052623499355247 10.1007/978-3-540-71333-3 10.1007/978-4-431-99490-9_5 10.1137/040613238 10.1007/978-3-642-02431-3 10.1016/j.na.2006.12.014 10.1006/jath.1996.3082 10.1137/S1052623402415846 10.1007/s10107-009-0323-4 10.1007/BF01891408 10.1007/978-3-540-24828-6 10.1007/s10107-012-0549-4 10.1007/3-540-31247-1 |
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| Copyright | Springer and Mathematical Optimization Society 2012 2014 INIST-CNRS Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2012 |
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| DOI | 10.1007/s10107-012-0550-y |
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| Keywords | Variational analysis Semi-infinite programming 49J53 Multiobjective optimization Qualification conditions Extremal principles Tangent and normal cones Secondary 90C30 Generalized differentiation Primary 49J52 Intersection Cone Existence theorem Multiobjective programming Semi infinite programming Non linear programming 49J53; Secondary 90C30 Infinite system Constrained optimization Extremum problem Qualification Nonsmooth analysis Variational calculus Optimality condition Optimality criterion Mathematical programming |
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| References | Bauschke, Borwein, Li (CR3) 1999; 86 Puente, Verade Serio (CR24) 1999; 7 Li, Ng (CR18) 2005; 16 Cánovas, López, Mordukhovich, Parra (CR5) 2009; 20 Borwein, Zhu (CR4) 2005 Cánovas, López, Mordukhovich, Parra (CR6) 2010; 20 Dinh, Mordukhovich, Nghia (CR10) 2010; 123 Rockafellar, Wets (CR25) 1998 Mordukhovich (CR22) 2006 Li, Ng (CR17) 2003; 14 Göpfert, Riahi, Tammer, Zalinescu (CR13) 2003 Schirotzek (CR26) 2007 Ernst, Théra (CR11) 2007; 18 Bao, Mordukhovich (CR1) 2010; 122 Deutsch, Li, Ward (CR8) 1997; 90 Goberna, Jeyakumar, Lopez (CR14) 2008; 68 Goberna, López (CR15) 1998 Jahn (CR16) 2004 Bao, Mordukhovich (CR2) 2010; 13 Fang, Li, Ng (CR12) 2010; 73 Li, Nahak, Singer (CR20) 2000; 11 CR23 Li, Ng, Pong (CR19) 2007; 18 Mordukhovich (CR21) 2006 Song, Zang (CR27) 2006; 106 Dinh, Mordukhovich, Nghia (CR9) 2009; 34 Chui, Deutsch, Ward (CR7) 1990; 6 N. Dinh (550_CR9) 2009; 34 C. Li (550_CR17) 2003; 14 D.H. Fang (550_CR12) 2010; 73 C. Li (550_CR19) 2007; 18 B.S. Mordukhovich (550_CR21) 2006 M.J. Cánovas (550_CR6) 2010; 20 T.Q. Bao (550_CR2) 2010; 13 R.T. Rockafellar (550_CR25) 1998 W. Schirotzek (550_CR26) 2007 F. Deutsch (550_CR8) 1997; 90 R. Puente (550_CR24) 1999; 7 H.H. Bauschke (550_CR3) 1999; 86 C.K. Chui (550_CR7) 1990; 6 A. Göpfert (550_CR13) 2003 J. Jahn (550_CR16) 2004 W. Li (550_CR20) 2000; 11 M.J. Cánovas (550_CR5) 2009; 20 M.A. Goberna (550_CR14) 2008; 68 M.A. Goberna (550_CR15) 1998 550_CR23 T.Q. Bao (550_CR1) 2010; 122 B.S. Mordukhovich (550_CR22) 2006 N. Dinh (550_CR10) 2010; 123 C. Li (550_CR18) 2005; 16 W. Song (550_CR27) 2006; 106 J.M. Borwein (550_CR4) 2005 E. Ernst (550_CR11) 2007; 18 |
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| Snippet | This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program
2011
)... Issue Title: Special Issue on Parametric Optimization - Recent Advances This paper contains selected applications of the new tangential extremal principles and... This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011)... |
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| SubjectTerms | Applied sciences Calculus Calculus of variations and optimal control Calculus of Variations and Optimal Control; Optimization Combinatorics Convex analysis Decision theory. Utility theory Exact sciences and technology Full Length Paper Intersections Mathematical analysis Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operational research and scientific management Operational research. Management science Optimization Principles Programming Sciences and techniques of general use Studies Theoretical |
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| Title | Tangential extremal principles for finite and infinite systems of sets II: applications to semi-infinite and multiobjective optimization |
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