On the Coderivative of the Projection Operator onto the Second-order Cone
The limiting (Mordukhovich) coderivative of the metric projection onto the second-order cone is computed. This result is used to obtain a sufficient condition for the Aubin property of the solution map of a parameterized second-order cone complementarity problem and to derive necessary optimality co...
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| Veröffentlicht in: | Set-valued analysis Jg. 16; H. 7-8; S. 999 - 1014 |
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| Sprache: | Englisch |
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01.12.2008
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| ISSN: | 0927-6947, 1572-932X |
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| Abstract | The limiting (Mordukhovich) coderivative of the metric projection onto the second-order cone
is computed. This result is used to obtain a sufficient condition for the Aubin property of the solution map of a parameterized second-order cone complementarity problem and to derive necessary optimality conditions for a mathematical program with a second-order cone complementarity problem among the constraints. |
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| AbstractList | The limiting (Mordukhovich) coderivative of the metric projection onto the second-order cone
is computed. This result is used to obtain a sufficient condition for the Aubin property of the solution map of a parameterized second-order cone complementarity problem and to derive necessary optimality conditions for a mathematical program with a second-order cone complementarity problem among the constraints. |
| Author | Outrata, Jiří V. Sun, Defeng |
| Author_xml | – sequence: 1 givenname: Jiří V. surname: Outrata fullname: Outrata, Jiří V. email: outrata@utia.cas.cz organization: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic – sequence: 2 givenname: Defeng surname: Sun fullname: Sun, Defeng organization: Department of Mathematics and Risk Management Institute, National University of Singapore |
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| Cites_doi | 10.1006/jmaa.1994.1144 10.1007/s10107-004-0538-3 10.1007/BF01455996 10.1287/moor.5.1.43 10.1287/moor.9.1.87 10.1023/A:1022996819381 10.1051/m2an:2004026 10.1007/BF00940933 10.1287/moor.28.1.39.14258 10.1016/S0024-3795(98)10032-0 10.1287/moor.25.1.1.15213 10.1137/S1052623400380365 10.1007/BFb0096285 10.1093/oso/9780198534778.001.0001 10.1007/978-3-642-02431-3 10.1007/s10957-008-9390-6 |
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| Keywords | Second-order cone 49J53 90C46 Primary: 49J52 Projection Aubin property Limiting coderivative Secondary: 58C06 |
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| References | Aubin (CR1) 1984; 9 Koecher, Brieg, Walcher (CR9) 1999 Robinson (CR18) 1980; 5 CR7 Mordukhovich (CR16) 2006 Scheel, Scholtes (CR20) 2000; 25 Clarke (CR4) 1983 Shapiro (CR21) 1990; 66 CR11 Lobo, Vandenberghe, Boyd, Lebret (CR12) 1998; 284 Chen, Chen, Tseng (CR2) 2004; 101 Rockafellar, Wets (CR19) 1998 Faraut, Korányi (CR5) 1994 Haslinger, Sassi (CR8) 2004; 38 Mordukhovich (CR15) 1994; 183 Fukushima, Luo, Tseng (CR6) 2002; 12 Chen, Sun, Sun (CR3) 2003; 25 Korányi (CR10) 1984; 269 Pang, Sun, Sun (CR17) 2003; 28 Mordukhovich (CR13) 1984; 28 Mordukhovich (CR14) 1988 B.S. Mordukhovich (92_CR14) 1988 B.S. Mordukhovich (92_CR15) 1994; 183 H. Scheel (92_CR20) 2000; 25 M. Fukushima (92_CR6) 2002; 12 A. Korányi (92_CR10) 1984; 269 S.M. Robinson (92_CR18) 1980; 5 X.-D. Chen (92_CR3) 2003; 25 A. Shapiro (92_CR21) 1990; 66 R.T. Rockafellar (92_CR19) 1998 B.S. Mordukhovich (92_CR13) 1984; 28 M.S. Lobo (92_CR12) 1998; 284 B.S. Mordukhovich (92_CR16) 2006 J.S. Pang (92_CR17) 2003; 28 92_CR7 J.-S. Chen (92_CR2) 2004; 101 F.H. Clarke (92_CR4) 1983 U. Faraut (92_CR5) 1994 M. Koecher (92_CR9) 1999 92_CR11 J. Haslinger (92_CR8) 2004; 38 J.-P. Aubin (92_CR1) 1984; 9 |
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is computed. This result is used to obtain a sufficient condition... |
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| Title | On the Coderivative of the Projection Operator onto the Second-order Cone |
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