Necessary conditions for vector optimization in infinite dimension

Marie Dvorská; Karel Pastor

Kybernetika (2015)

  • Volume: 51, Issue: 6, page 1023-1034
  • ISSN: 0023-5954

Abstract

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In the paper we present second-order necessary conditions for constrained vector optimization problems in infinite-dimensional spaces. In this way we generalize some corresponding results obtained earlier.

How to cite

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Dvorská, Marie, and Pastor, Karel. "Necessary conditions for vector optimization in infinite dimension." Kybernetika 51.6 (2015): 1023-1034. <http://eudml.org/doc/276287>.

@article{Dvorská2015,
abstract = {In the paper we present second-order necessary conditions for constrained vector optimization problems in infinite-dimensional spaces. In this way we generalize some corresponding results obtained earlier.},
author = {Dvorská, Marie, Pastor, Karel},
journal = {Kybernetika},
keywords = {$C^\{1\{\},1\}$–function; $\{\ell \}$–stable function; generalized second-order directional derivative; Dini derivative; vector optimization},
language = {eng},
number = {6},
pages = {1023-1034},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Necessary conditions for vector optimization in infinite dimension},
url = {http://eudml.org/doc/276287},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Dvorská, Marie
AU - Pastor, Karel
TI - Necessary conditions for vector optimization in infinite dimension
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 6
SP - 1023
EP - 1034
AB - In the paper we present second-order necessary conditions for constrained vector optimization problems in infinite-dimensional spaces. In this way we generalize some corresponding results obtained earlier.
LA - eng
KW - $C^{1{},1}$–function; ${\ell }$–stable function; generalized second-order directional derivative; Dini derivative; vector optimization
UR - http://eudml.org/doc/276287
ER -

References

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  1. Bednařík, D, Berková, A, On some properties of l-stable functions., In: Proc.14th WSEAS International Conference on Mathematical Methods, Comput. Techniques and Intelligent Systems (A. J. Viamonte, ed.), Porto 2012, pp. 52-55. 
  2. Bednařík, D., Pastor, K., 10.1137/s0363012903424174, SIAM J. Control Optim. 43 (2004), 1063-1077. Zbl1089.49023MR2114389DOI10.1137/s0363012903424174
  3. Bednařík, D., Pastor, K., 10.1007/s10107-007-0094-8, Math. Programming, Ser. A 113 (2008), 283-298. Zbl1211.90276MR2375484DOI10.1007/s10107-007-0094-8
  4. Bednařík, D., Pastor, K., 10.1016/j.na.2007.09.006, Nonlinear Analysis 69 (2008), 3128-3135. Zbl1146.49017MR2452120DOI10.1016/j.na.2007.09.006
  5. Bednařík, D., Pastor, K., 10.1016/j.na.2008.03.011, Nonlinear Analysis 70 (2009), 2317-2324. Zbl1158.49022MR2498316DOI10.1016/j.na.2008.03.011
  6. Bednařík, D., Pastor, K., 10.1016/j.na.2009.01.035, Nonlinear Analysis 71 (2009), 1964-1969. MR2524410DOI10.1016/j.na.2009.01.035
  7. Bednařík, D., Pastor, K., 10.1016/j.na.2009.08.004, Nonlinear Analysis 72 (2010), 1198-1209. MR2577520DOI10.1016/j.na.2009.08.004
  8. Bednařík, D., Pastor, K., 10.1016/j.na.2010.10.009, Nonlinear Analysis 74 (2011), 1372-1382. MR2746815DOI10.1016/j.na.2010.10.009
  9. Cominetti, R., Correa, R., 10.1137/0328045, SIAM J. Control Optim. 28 (1990), 789-809. Zbl0714.49020MR1051624DOI10.1137/0328045
  10. Chan, W. L., Huang, L. R., Ng, K. F., 10.1137/s0363012992227423, SIAM J. Control Optim. 32 (1994), 591-611. Zbl0801.49016MR1269984DOI10.1137/s0363012992227423
  11. Dvorská, M., Pastor, K., 10.2478/s12175-014-0252-4, Mathematica Slovaca 64 (2014), 1-18. MR3255866DOI10.2478/s12175-014-0252-4
  12. Dvorská, M., Pastor, K., 10.1007/s40306-015-0129-9, Acta Mathematica Vietnamica, accepted. DOI10.1007/s40306-015-0129-9
  13. Fabian, M, Hájek, P., Habala, P., Santalucía, V. M., Pelant, J., Zizler, V., 10.1007/978-1-4757-3480-5, Springer-Verlag, New York 2001. Zbl0981.46001MR1831176DOI10.1007/978-1-4757-3480-5
  14. Ginchev, I., 10.1016/j.na.2010.08.032, Nonlinear Analysis 74 (2011), 182-194. Zbl1205.26007MR2734988DOI10.1016/j.na.2010.08.032
  15. Ginchev, I., Guerraggio, A., 10.1080/02331930903578718, Optimization 60 (2011), 179-199. Zbl1237.90221MR2772143DOI10.1080/02331930903578718
  16. Ginchev, I., Guerraggio, A., Rocca, M., 10.1007/s10492-006-0002-1, Applications of Mathematics 51 (2006), 5-36. Zbl1164.90399MR2197320DOI10.1007/s10492-006-0002-1
  17. Ginchev, I., Guerraggio, A., Rocca, M., 10.1007/s10107-005-0621-4, Math. Programming, Ser. B 104 (2005), 389-405. MR2179243DOI10.1007/s10107-005-0621-4
  18. Ginchev, I., Guerraggio, A., Rocca, M., 10.1007/0-387-24276-7_27, In: Variational Analysis and Applications (F. Gianessi, A. Maugeri, ed.), Kluwer Academic, London 2005, pp. 427-450. Zbl1148.90011MR2159985DOI10.1007/0-387-24276-7_27
  19. Guerraggio, A., Luc, D. T., 10.1023/a:1017519922669, J. Optim. Theory Appl. 109 (2001), 615-629. Zbl1038.49027MR1835076DOI10.1023/a:1017519922669
  20. Guerraggio, A., Luc, D. T., 10.1023/a:1022114319999, J. Optim. Theory Appl. 116 (2003), 117-129. Zbl1030.90115MR1961031DOI10.1023/a:1022114319999
  21. Georgiev, P. G., Zlateva, N. P., 10.1007/bf00425960, Set-Valued Analysis 4 (1996), 101-117. MR1394408DOI10.1007/bf00425960
  22. Hiriart-Urruty, J. B., Strodiot, J. J., Nguyen, V. H., 10.1007/bf01442169, Appl. Math. Comput. 11 (1984), 43-56. MR0726975DOI10.1007/bf01442169
  23. Jahn, J., 10.1007/978-3-540-24828-6, Springer-Verlag, Berlin 2004. Zbl1298.90092MR2058695DOI10.1007/978-3-540-24828-6
  24. Jameson, G., 10.1007/bfb0059130, Springer-Verlag, Berlin 1970. Zbl0234.46007MR0438077DOI10.1007/bfb0059130
  25. Jeyakumar, V., Luc, D. T., Nonsmooth Vector Functions and Continuous Optimization., Springer-Verlag, Berlin 2008. Zbl1138.90002MR2354918
  26. Khanh, P. Q., Tuan, N. D., 10.1007/s10957-006-9103-y, J. Optim. Theory Appl. 130 (2006), 289-308. Zbl1143.90386MR2282352DOI10.1007/s10957-006-9103-y
  27. Khanh, P. Q., Tuan, N. D., 10.1007/s10957-007-9169-1, J. Optim. Theory Appl. 133 (2007), 341-357. Zbl1149.90134MR2333819DOI10.1007/s10957-007-9169-1
  28. Khanh, P. Q., Tuan, N. D., 10.1016/j.jmaa.2012.12.076, J. Math. Anal. Appl. 403 (2013), 695-702. MR3037499DOI10.1016/j.jmaa.2012.12.076
  29. Khanh, P. Q., Tuan, N. D., 10.1016/j.jmaa.2012.12.075, J. Math. Anal. Appl. 403 (2013), 703-714. Zbl1291.90225MR3037500DOI10.1016/j.jmaa.2012.12.075
  30. Li, S. J., Xu, S., 10.1080/01630563.2010.490970, Numer. Funct. Anal. Optim. 31 (2010), 715-727. Zbl1218.90214MR2682838DOI10.1080/01630563.2010.490970
  31. Mordukhovich, B. S., Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications., Springer-Verlag, Berlin 2006. Zbl1100.49002MR2191744
  32. Mordukhovich, B. S., Treiman, J. S., Zhu, Q. J., 10.1137/s1052623402414701, SIAM J. Optim. 14 (2003), 359-379. MR2048166DOI10.1137/s1052623402414701
  33. Pastor, K., 10.11650/tjm.18.2014.2605, Taiwan. J. Math. 18 (2014), 187-197. MR3162119DOI10.11650/tjm.18.2014.2605
  34. Rockafellar, R. T., 10.1515/9781400873173, Princeton University Press, Princeton 1970. Zbl1011.49013MR0274683DOI10.1515/9781400873173
  35. Rockafellar, R. T., Wets, J. B., 10.1007/978-3-642-02431-3, Springer-Verlag, New York 1998. Zbl0888.49001MR1491362DOI10.1007/978-3-642-02431-3

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