A Steepest Descent-Like Method for Variable Order Vector Optimization Problems
In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimizat...
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| Published in | Journal of optimization theory and applications Vol. 162; no. 2; pp. 371 - 391 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.08.2014
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-3239 1573-2878 |
| DOI | 10.1007/s10957-013-0308-6 |
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| Abstract | In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case. |
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| AbstractList | In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case.[PUBLICATION ABSTRACT] In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case. |
| Author | Bello Cruz, J. Y. Bouza Allende, G. |
| Author_xml | – sequence: 1 givenname: J. Y. surname: Bello Cruz fullname: Bello Cruz, J. Y. organization: Universidade Federal de Goiás – sequence: 2 givenname: G. surname: Bouza Allende fullname: Bouza Allende, G. email: gema@matcom.uh.cu organization: Facultad de Matemática y Computación, Universidad de La Habana |
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| Cites_doi | 10.1080/02331934.2010.522710 10.1016/j.na.2011.04.067 10.1016/j.cam.2004.06.018 10.1007/s001860050021 10.1137/S1052623403429093 10.1007/s001860000043 10.1007/s10107-006-0071-7 10.1016/j.na.2010.06.051 10.1007/s10957-011-9928-x 10.1007/BF02592221 10.1023/B:COAP.0000018877.86161.8b 10.1007/s10898-007-9246-x 10.1287/moor.19.4.790 10.1137/0334031 10.1007/BF01109805 10.1137/08071692X 10.1007/978-3-540-24828-6 10.1007/BF00939046 10.1080/02331939508844042 10.1007/978-1-4419-0158-3_23 10.1016/j.camwa.2006.08.014 10.1007/978-3-642-50280-4 10.1007/978-0-387-77247-9_18 |
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| Keywords | Gradient-like method Convexity Variable order Vector optimization Weakly efficient points |
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| SubjectTerms | Algorithms Analysis Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Engineering Mathematical analysis Mathematics Mathematics and Statistics Medical diagnosis Operations Research/Decision Theory Optimization Sequences Studies Theory of Computation Vectors (mathematics) |
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| Title | A Steepest Descent-Like Method for Variable Order Vector Optimization Problems |
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