DOI QR코드

DOI QR Code

SEQUENTIAL OPTIMALITY THEOREMS FOR SECOND-ORDER CONE LINEAR FRACTIONAL VECTOR OPTIMIZATION PROBLEMS

  • Moon Hee Kim (College of General Education, Tongmyong University)
  • Received : 2023.04.10
  • Accepted : 2023.08.14
  • Published : 2023.09.30

Abstract

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2C1003309).

References

  1. R.S. Burachik and V. Jeyakumar, Dual condition for the convex subdifferential sum formula with applications, J. Con. Analy., 12(2005), 279-290.
  2. E.V. Choo, Proper efficiency and linear fractional vector optimization, Oper. Res. 32(1984), 216-220. https://doi.org/10.1287/opre.32.1.216
  3. K.L. Chew and E.V. Choo, Pseudolinearity and efficiency, Math. Programming 28(1984), 226-239. https://doi.org/10.1007/BF02612363
  4. B. D. Craven, "Fractional Programming", Heldermann Verlag, Berlin, 1988.
  5. B. D. Craven and B. Mond, The dual of a fractional linear program, J. Math. Anal. Appl., 42 (1973), 507-512. https://doi.org/10.1016/0022-247X(73)90158-3
  6. M. Ehrgott, Multicriteria Optimization, Lecture Notes in Economics and Mathematical Systems 491, Springer-Verlag Berlin Heidelberg, 2000.
  7. A.M. Geoffrion, Proper efficiency and the theory of vector optimization, Journal of Mathematical Analysis and Applications, 22(1968), 618-630. https://doi.org/10.1016/0022-247X(68)90201-1
  8. H. Isermann, Proper efficiency and the linear vector maximum problem, Oper. Res., 22(1974), no. 1, 189-191.
  9. J. Jeyakumar, G. M. Lee and N. Dinh, New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs, SIAM J. Optim., 14 (2003), 534-547. https://doi.org/10.1137/S1052623402417699
  10. V. Jeyakumar, S. Kum and G. M. Lee, Necessary and sufficient conditions for Farkas' Lemma for cone systems and second-order cone programming duality, J. Convex Anal. 15(2008), 63-71.
  11. M.H. Kim and G.M. Lee, On efficient solutions for semidefinite linear fractional vector optimization problems, to appear in Minimax Theory and its Applications.
  12. M. H. Kim, G. S. Kim and G. M. Lee, On weakly efficient solutions for semidefinite linear fractional vector optimization problems, to appear in J. Nonlinear and Convex Anal..
  13. G.Y. Li, V. Jeyakumar and G.M. Lee, Robust conjugate duality for convex optimization under uncertainty with application to data classification, Nonlinear Anal., 74(2011), 2327-2341. https://doi.org/10.1016/j.na.2010.11.036
  14. Y. Sawaragi, H. Nakayama and T. Tanino, "Theory of Multiobjective Optimization", Academic Press Inc., 1985.