Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 62, 2013 - Issue 1
288
Views
3
CrossRef citations to date
0
Altmetric
Articles

Well-posedness and stability in vector optimization problems using Henig proper efficiency

&
Pages 155-165 | Received 06 Nov 2010, Accepted 04 May 2011, Published online: 27 Jun 2011

References

  • Bednarczuk , E . 1987 . “ Well-posedness of vector optimization problems ” . In Recent Advances and Historical Development of Vector Optimization Problems , Edited by: Jahn , J and Krabs , W . Vol. 294 , 51 – 61 . Berlin : Lecture Notes in Economics and Mathematical Systems, Springer Verlag .
  • Bednarczuk , E . 1994 . An approach to well-posedness in vector optimization: Consequence to stability, parametric optimization . Control Cybernet. , 23 : 107 – 122 .
  • Bednarczuk , E and Song , W . 1998 . PC Points and their applications to vector optimization . Pliska Stud. Math. Bulgar. , 12 : 21 – 30 .
  • Benson , HP . 1979 . An improved definition of proper efficiency for vector maximization with respect to cones . J. Math. Anal. Appl. , 71 : 232 – 241 .
  • Borwein , J . 1977 . Proper efficient points for maximizations with respect to cones . SIAM J. Control Optim. , 15 : 57 – 63 .
  • Dontchev , AL and Zolezzi , T . 1993 . Well-Posed Optimization Problems, Lecture Notes in Mathematics , Vol. 1543 , Berlin , , Germany : Springer-Verlag .
  • Durea , M . 2007 . Scalarization for pointwise well-posed vectorial problems . Math. Methods Oper. Res. , 66 : 409 – 418 .
  • Geoffrion , AM . 1968 . Proper efficiency and the theory of vector maximization . J. Math. Anal. Appl. , 22 : 613 – 630 .
  • Hadamard , J . 1902 . Sur les problèmes aux dérivés partielles et leur signification physique . Princeton Univ. Bull. , 13 : 49 – 52 .
  • Henig , MI . 1982 . Proper efficiency with respect to cones . J. Optim. Theory Appl. , 36 : 387 – 407 .
  • Huang , XX . 2001 . Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle . J. Optim. Theory Appl. , 108 : 671 – 684 .
  • Kuhn , HW and Tucker , AW . 1951 . “ Nonlinear programming ” . In Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability , Edited by: Neyman , J . 481 – 492 . Berkeley , , California : University of California Press .
  • Loridan , P . 1995 . “ Well-posedness in vector optimization ” . In Recent Developments in Well-Posed Variational Problems , Edited by: Lucchetti , R and Revalski , J . Vol. 331 , 171 – 192 . Dordrecht : Mathematics and Its Applications, Math. Appl. Kluwer Academic Publishers .
  • Lucchetti , R . 1987 . “ Well-posedness towards vector optimization ” . In Recent Advances and Historical Development of Vector Optimization Problems , Edited by: Jahn , J and Krabs , W . Vol. 294 , 194 – 207 . Berlin : Lecture Notes in Economics and Mathematical Systems, Springer Verlag .
  • Lucchetti , R . 2006 . Convexity and Well-Posed Problems, CMS Books in Mathematics , New York : Springer .
  • Lucchetti , RE and Miglierina , E . 2004 . Stability for convex vector optimization problems . Optimization , 53 : 517 – 528 .
  • Miglierina , E and Molho , E . 2002 . Scalarization and stability in vector optimization . J. Optim. Theory Appl. , 114 : 657 – 670 .
  • Miglierina , E and Molho , E . 2003 . Well-posedness and convexity in vector optimization . Math. Methods Oper. Res. , 58 : 375 – 385 .
  • Miglierina , E , Molho , E and Rocca , M . 2005 . Well-posedness and scalarization in vector optimization . J. Optim. Theory Appl. , 126 : 391 – 409 .
  • Naccache , PH . 1979 . Stability in multicriteria optimization . J. Math. Anal. Appl. , 68 : 441 – 453 .
  • Nakayama , H , Sawaragi , Y and Tanino , T . “ Theory of Multiobjective Optimization ” . In Mathematics in Science and Engineering , Vol. 176 , Orlando , , Florida : Academic Press Inc. .
  • Tanino , T . 1988 . Stability and sensitivity analysis in convex vector optimization . SIAM J. Control Optim. , 26 : 521 – 536 .
  • Tykhonov , AN . 1966 . On the stability of the functional optimization problem . USSR, Comput. Math. Math. Phys. , 6 : 28 – 33 .
  • Zheng , XY . 1998 . Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces . J. Optim. Theory Appl. , 96 : 221 – 233 .

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.