Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 63, 2014 - Issue 5
381
Views
26
CrossRef citations to date
0
Altmetric
Articles

A quadratically convergent Newton method for vector optimization

, &
Pages 661-677 | Received 17 Jun 2011, Accepted 08 May 2012, Published online: 13 Jun 2012

References

  • Aliprantis , CD , Florenzano , M , Martins da Rocha , VF and Tourky , R . 2004 . General equilibrium in infinite security markets . J. Math. Econ. , 40 : 683 – 699 .
  • Aliprantis , CD , Florenzano , M and Tourky , R . 2004 . General equilibrium analysis in ordered topological vector spaces . J. Math. Econ. , 40 : 247 – 269 .
  • Bertsekas , D . 2003 . Convex Analysis and Optimization , Belmont : Athena Scientific .
  • Bonnel , H , Iusem , AN and Svaiter , BF . 2005 . Proximal methods in vector optimization . SIAM J. Optim. , 15 : 953 – 970 .
  • Cornet , B . 1977 . Accessibilité des optimums de Pareto par des processus monotones . C. R. Acad. Sci. Paris Sér. A-B , 285 : A641 – A644 .
  • Cornet , B . 1977 . On Planning Procedures Defined by Multivalued Differential Equations . Systemes Dynamiques et Modèles Economiques, Colloques Internationaux de C.N.R.S. , No. 295 : 111 – 122 .
  • Fliege , J , Graña Drummond , LM and Svaiter , BF . 2009 . Newton's method for mutiobjective optimization . SIAM J. Optim. , 20 : 602 – 626 .
  • Fliege , J and Svaiter , BF . 2000 . Steepest descent methods for multicriteria optimization . Math. Meth. Oper. Res. , 51 : 479 – 494 .
  • Fukuda , EH and Graña Drummond , LM . 2011 . On the convergence of the projected gradient method for vector optimization . Optimization , 60 : 1009 – 1021 .
  • Graña Drummond , LM and Iusem , AN . 2004 . A projected gradient method for vector optimization problems . Comput. Optim. Appl. , 28 : 5 – 29 .
  • Graña Drummond , LM and Svaiter , BF . 2005 . A steepest descent method for vector optimization . J. Comput. Appl. Math. , 175 : 395 – 414 .
  • Henry , C . 1974 . Problèmes d'existence et de stabilité pour des processus dynamiques considérés en économie mathématique . C. R. Acad. Sci. Paris Sér. A , 278 : 97 – 100 .
  • Jahn , J . 2004 . Vector Optimization , Berlin : Springer .
  • Miettinen , KM . 1999 . Nonlinear Multiobjective Optimization , Norwell : Kluwer Academic .
  • Rockafellar , RT . 1972 . Convex Analysis , Princeton : Princeton University Press .
  • Sawaragi , H and Tanino , T . 1985 . Theory of Multiobjective Optimization , Orlando : Academic Press .
  • The Luc , D . 1989 . Theory of Vector Optimization , Berlin : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.