Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1 , 1 data

Liping Liu; Pekka Neittaanmäki; Michal Křížek

Applications of Mathematics (2000)

  • Volume: 45, Issue: 5, page 381-397
  • ISSN: 0862-7940

Abstract

top
We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C 1 , 1 . Second-order optimality conditions for local Pareto solutions are derived as a special case.

How to cite

top

Liu, Liping, Neittaanmäki, Pekka, and Křížek, Michal. "Second-order optimality conditions for nondominated solutions of multiobjective programming with $C^{1,1}$ data." Applications of Mathematics 45.5 (2000): 381-397. <http://eudml.org/doc/33066>.

@article{Liu2000,
abstract = {We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class $C^\{1,1\}$. Second-order optimality conditions for local Pareto solutions are derived as a special case.},
author = {Liu, Liping, Neittaanmäki, Pekka, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {multiobjective programming; nonsmooth constrained optimization; second-order optimality conditions; nondominated solutions; local Pareto optimal solutions; multiobjective programming; nonsmooth constrained optimization; second-order optimality conditions; nondominated solutions; local Pareto optimal solutions},
language = {eng},
number = {5},
pages = {381-397},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Second-order optimality conditions for nondominated solutions of multiobjective programming with $C^\{1,1\}$ data},
url = {http://eudml.org/doc/33066},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Liu, Liping
AU - Neittaanmäki, Pekka
AU - Křížek, Michal
TI - Second-order optimality conditions for nondominated solutions of multiobjective programming with $C^{1,1}$ data
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 5
SP - 381
EP - 397
AB - We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class $C^{1,1}$. Second-order optimality conditions for local Pareto solutions are derived as a special case.
LA - eng
KW - multiobjective programming; nonsmooth constrained optimization; second-order optimality conditions; nondominated solutions; local Pareto optimal solutions; multiobjective programming; nonsmooth constrained optimization; second-order optimality conditions; nondominated solutions; local Pareto optimal solutions
UR - http://eudml.org/doc/33066
ER -

References

top
  1. Foundations of Optimization, LN in Econom. and Math. Systems, vol. 122, Springer-Verlag, Berlin-Heidelberg-New York, 1976. (1976) MR0429122
  2. 10.1007/BF00934107, J. Optim. Theory Appl. 31 (1980), 143–165. (1980) MR0600379DOI10.1007/BF00934107
  3. A New Approach to Second Order Optimality Conditions in Vector Optimization, Advances in Multiple Objective and Goal Programming, LN in Econom. and Math. Systems, vol. 455, Springer, Berlin, 1997. MR1487397
  4. 10.1007/BF01442169, Appl. Math. Optim. 11 (1984), 43–56. (1984) MR0726975DOI10.1007/BF01442169
  5. Second-order conditions for nondominated solution in generalized multiobjective mathematical programming, J. Systems Sci. Math. Sci. 5 (1985), 172–184. (Chinese) (1985) MR0847811
  6. 10.1080/02331938808843333, Optimization 19 (1988), 169–179. (1988) MR0948388DOI10.1080/02331938808843333
  7. Finite Element Approximation of Variational Problems and Applications, Longman, Harlow, 1990. (1990) MR1066462
  8. The second-order conditions of nondominated solutions for C 1 , 1 generalized multiobjective mathematical programming, J. Systems Sci. Math. Sci. 4 (1991), 128–138. (1991) MR1119288
  9. The second order conditions for C 1 , 1 nonlinear mathematical programming, pp. 153–158. MR1703473
  10. 10.1023/A:1023068513188, Appl. Math. 42 (1997), 311–320. (1997) MR1453935DOI10.1023/A:1023068513188
  11. 10.1137/0805032, SIAM J. Optim. 5 (1995), 659–669. (1995) MR1344674DOI10.1137/0805032
  12. First and second order optimality conditions in vector optimization, Ann. Sci. Math. Québec 14 (1990), 65–79. (1990) MR1070607
  13. 10.1137/0115056, SIAM. J. Appl. Math. 15 (1967), 641–652. (1967) Zbl0166.15601MR0216866DOI10.1137/0115056
  14. Nonlinear Multiobjective Optimization, Kluwer, Dordrecht, 1998. (1998) MR1784937
  15. Theory of the Integral, Hafner Publishing Co., New York, 1937. (1937) 
  16. 10.1080/01630569108816425, Numer. Funct. Anal. Optim. 12 (1991), 237–252. (1991) MR1125051DOI10.1080/01630569108816425
  17. 10.1007/BF02207780, J. Optim. Theory Appl. 80 (1994), 551–571. (1994) Zbl0797.90101MR1265176DOI10.1007/BF02207780
  18. 10.1006/jmaa.1995.1247, J. Math. Anal. Appl. 193 (1995), 465–482. (1995) MR1338716DOI10.1006/jmaa.1995.1247
  19. 10.1016/0362-546X(94)90218-6, Nonlinear Anal. 23 (1994), 767–784. (1994) Zbl0816.49008MR1298568DOI10.1016/0362-546X(94)90218-6
  20. 10.1080/02331939208843851, Optimization 26 (1992), 165–185. (1992) MR1236606DOI10.1080/02331939208843851
  21. 10.1023/A:1022695714596, J. Optim. Theory Appl. 95 (1997), 209–224. (1997) MR1477357DOI10.1023/A:1022695714596
  22. Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjective, J. Optim. Theory Appl. 17 (1974), 320–377. (1974) MR0381739
  23. Multiple-Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, 1985. (1985) MR0812059

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.