Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems
The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990 ), we obtain the Lagrangian condition for approximate solutions on set-value...
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| Vydáno v: | Optimization letters Ročník 7; číslo 8; s. 1847 - 1856 |
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| Jazyk: | angličtina |
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01.12.2013
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| ISSN: | 1862-4472, 1862-4480 |
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| Abstract | The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320,
1990
), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative. |
|---|---|
| AbstractList | The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320,
1990
), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative. |
| Author | Zeng, J. Li, X. B. Long, X. J. |
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| Cites_doi | 10.1080/02331939708844332 10.1016/j.na.2011.09.024 10.1287/moor.4.1.79 10.1007/BF00941179 10.1007/978-3-540-24828-6 10.1007/BF00940762 10.1137/060651860 10.1007/BF00936165 10.1007/s00186-005-0007-7 10.1007/BF00940478 10.1080/02331930903531527 10.1007/s10957-011-9891-6 10.1007/s10898-008-9336-4 10.1016/j.jmaa.2005.03.011 10.1016/j.na.2011.03.015 10.1016/S0022-247X(03)00360-3 10.1007/s10898-009-9452-9 10.1007/s10107-004-0569-9 10.1007/s10957-009-9609-1 10.1007/s00186-006-0079-z 10.1007/978-3-642-02431-3 10.1007/s10107-008-0249-2 10.1007/s10957-010-9657-6 10.1007/3-540-31247-1 10.1007/978-1-4419-0158-3_21 |
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| Keywords | Mordukhovich coderivative Lagrangian condition Nonconvex set-valued optimization Approximate solution |
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| References | Mordukhovich (CR24) 2006 Dutta, Tammer (CR10) 2006; 64 Gao, Hou, Yang (CR11) 2012; 152 Taa (CR27) 2005; 62 Zheng, Ng (CR31) 2006; 17 Göpfert, Riahi, Tammer, Zălinescu (CR14) 2003 Bao, Mordukhovich (CR2) 2009; 43 Bao, Mordukhovich (CR3) 2010; 122 Chen, Huang, Yang (CR5) 2005 CR16 Ha (CR17) 2012; 75 Luc (CR22) 1989 Loridan (CR21) 1984; 43 Gong, Dong, Wang (CR13) 2003; 284 Amahroq, Taa (CR1) 1997; 41 Durea, Dutta, Tammer (CR8) 2010; 145 Durea, Strugariu (CR9) 2011; 60 Jahn (CR19) 2004 Mordukhovich (CR23) 2006 Hiriart-Urruty (CR18) 1979; 4 CR6 Clarke (CR7) 1983 Gerth, Weidner (CR12) 1990; 67 Rockafellar, Wets (CR26) 1998 Vályi (CR28) 1987; 55 Kutateladze (CR20) 1979; 20 Bao, Tammer (CR4) 2012; 75 Ha (CR15) 2005; 311 Qiu, Yang (CR25) 2010; 47 Zheng, Ng (CR30) 2005; 104 White (CR29) 1986; 49 J. Jahn (527_CR19) 2004 X.Y. Zheng (527_CR30) 2005; 104 T.Q. Bao (527_CR2) 2009; 43 R.T. Rockafellar (527_CR26) 1998 T.X.D. Ha (527_CR15) 2005; 311 Y. Gao (527_CR11) 2012; 152 D.J. White (527_CR29) 1986; 49 F.H. Clarke (527_CR7) 1983 A. Göpfert (527_CR14) 2003 G.Y. Chen (527_CR5) 2005 B.S. Mordukhovich (527_CR24) 2006 C. Gerth (527_CR12) 1990; 67 527_CR6 D.T. Luc (527_CR22) 1989 I. Vályi (527_CR28) 1987; 55 X.Y. Zheng (527_CR31) 2006; 17 T.X.D. Ha (527_CR17) 2012; 75 X.H. Gong (527_CR13) 2003; 284 T.Q. Bao (527_CR4) 2012; 75 T. Amahroq (527_CR1) 1997; 41 A. Taa (527_CR27) 2005; 62 T.Q. Bao (527_CR3) 2010; 122 Q.S. Qiu (527_CR25) 2010; 47 J. Durea (527_CR8) 2010; 145 J. Durea (527_CR9) 2011; 60 527_CR16 J.B. Hiriart-Urruty (527_CR18) 1979; 4 S.S. Kutateladze (527_CR20) 1979; 20 Loridan (527_CR21) 1984; 43 B.S. Mordukhovich (527_CR23) 2006 J. Dutta (527_CR10) 2006; 64 |
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| Title | Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems |
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