Generalized Proximal Method for Efficient Solutions in Vector Optimization
This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed conv...
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| Veröffentlicht in: | Numerical functional analysis and optimization Jg. 32; H. 8; S. 843 - 857 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia, PA
Taylor & Francis Group
01.08.2011
Taylor & Francis |
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| ISSN: | 0163-0563, 1532-2467 |
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| Abstract | This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed convex cone. In contrast to most published literature on this subject, our algorithm does not depend on the nonemptiness of ordering cone of the space under consideration and deals with finding efficient solutions of the vector optimization problem in question. We prove that under some suitable conditions the sequence generated by our method weakly converges to an efficient solution of this problem. |
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| AbstractList | This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed convex cone. In contrast to most published literature on this subject, our algorithm does not depend on the nonemptiness of ordering cone of the space under consideration and deals with finding efficient solutions of the vector optimization problem in question. We prove that under some suitable conditions the sequence generated by our method weakly converges to an efficient solution of this problem. |
| Author | Chuong, T. D. |
| Author_xml | – sequence: 1 givenname: T. D. surname: Chuong fullname: Chuong, T. D. email: chuongthaidoan@yahoo.com organization: Department of Mathematics & Applications , Saigon University |
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| Cites_doi | 10.1007/3-540-31246-3 10.1023/B:COAP.0000018877.86161.8b 10.1007/s001860000043 10.1007/978-1-4612-1394-9 10.1023/A:1004695229456 10.1016/j.cam.2004.06.018 10.1016/j.ejor.2006.09.070 10.1142/9789812777096 10.1137/S1052623403429093 10.1007/s10957-010-9667-4 10.1137/S105262340139611X 10.1016/j.camwa.2008.11.017 10.1080/01630560902735272 |
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| Keywords | Generalized proximal method 65K05 Efficient solution Uniformly smooth Optimization method Banach space Algorithm Weak convergence Numerical analysis 49J52 90C25 Ordering Variational calculus Uniformly convex Vector optimization Mathematical programming 49M99 |
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| References | Alber Y. (CIT0001) 2006 CIT0021 Chuong T. D. (CIT0009) CIT0012 Jahn J. (CIT0016) 1999 Gopfert A. (CIT0013) 2003 Phelps R.R. (CIT0020) 1993; 1364 Chen Z. (CIT0008); 57 Ehrgott M. (CIT0011) 2005 Mordukhovich B.S. (CIT0019) 2006 CIT0003 CIT0014 CIT0002 CIT0005 CIT0004 CIT0015 Luc D.T. (CIT0018) 1989 CIT0007 CIT0006 CIT0017 |
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| SubjectTerms | Algorithms Banach space Calculus of variations and optimal control Efficient solution Exact sciences and technology Functional analysis Generalized proximal method Mapping Mathematical analysis Mathematical models Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Sciences and techniques of general use Uniformly convex Uniformly smooth Vector optimization Vectors (mathematics) |
| Title | Generalized Proximal Method for Efficient Solutions in Vector Optimization |
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