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DOI QR Code

SOLUTION SETS OF SECOND-ORDER CONE LINEAR FRACTIONAL OPTIMIZATION PROBLEMS

  • Kim, Gwi Soo (Department of Applied Mathematics, Pukyong National University) ;
  • Kim, Moon Hee (College of General Education, Tongmyong University) ;
  • Lee, Gue Myung (Department of Applied Mathematics, Pukyong National University)
  • Received : 2020.07.03
  • Accepted : 2020.10.12
  • Published : 2021.03.15

Abstract

We characterize the solution set for a second-order cone linear fractional optimization problem (P). We present sequential Lagrange multiplier characterizations of the solution set for the problem (P) in terms of sequential Lagrange multipliers of a known solution of (P).

Keywords

References

  1. F. Alizadeh and D. Goldfarb, Second-order cone programming, ISMP 2000, Part 3 (Atlanta, GA), Math. Program., 95 (2003), Ser. B, 3-51. https://doi.org/10.1007/s10107-002-0339-5
  2. M.H. Kim, G.S. Kim and G.M. Lee, On semidefinite linear fractional optimization problems, accepted for publication.
  3. G.S. Kim, M.H. Kim and G.M. Lee, On optimality and duality for second-order cone linear fractional optimization problems, accepted for publication.
  4. V. 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
  5. V. Jeyakumar, G.M. Lee and N. Dinh, Lagrange multiplier conditions characterizing optimal solution sets of cone-constrained convex programs, J. Optim. Theory Appl., 123 (2004), 83-103. https://doi.org/10.1023/B:JOTA.0000043992.38554.c8
  6. J.V. Burke and M. Ferris, Characterization of solution sets of convex programs, Oper. Res. Lett., 10 (1991), 57-60. https://doi.org/10.1016/0167-6377(91)90087-6
  7. M. Castellani and M. Giuli, A characterization of the solution set of pseudoconvex extremum problems, J. Convex Anal., 19 (2012), 113-123.
  8. V. Jeyakumar, G.M. Lee and N. Dinh, Lagrange multiplier conditions characterizing optimal solution sets of cone-constrained convex programs, J. Optim. Theory Appl., 123 (2004), 83-103. https://doi.org/10.1023/B:JOTA.0000043992.38554.c8
  9. V. Jeyakumar, G.M. Lee and N. Dinh, Characterizations of solution sets of convex vector minimization problems, Eur. J. Oper. Res., 174 (2006), 1380-1395. https://doi.org/10.1016/j.ejor.2005.05.007
  10. V. Jeyakumar, G,M. Lee and G. Li, Characterizing robust solution sets of convex programs under data uncertainty, J. Optim. Theory Appl., 164 (2015), 407-435. https://doi.org/10.1007/s10957-014-0564-0
  11. V. Jeyakumar and X.Q. Yang, On characterizing the solution sets of pseudolinear programs, J. Optim. Theory Appl. 87 (1995), 747-755. https://doi.org/10.1007/BF02192142
  12. C.S. Lalitha and M. Mehta, Characterizations of solution sets of mathematical programs in terms of Lagrange multipliers, Optimization, 58 (2009), 995-1007. https://doi.org/10.1080/02331930701763272
  13. O.L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 7 (1988), 21-26. https://doi.org/10.1016/0167-6377(88)90047-8
  14. J.P. Penot, Characterization of solution sets of quasiconvex programs, J. Optim. Theory Appl., 117 (2003), 627-636. https://doi.org/10.1023/A:1023905907248
  15. T.Q. Son and N. Dinh, Characterizations of optimal solution sets of convex infinite programs, TOP. 16 (2008), 147-163. https://doi.org/10.1007/s11750-008-0039-2
  16. Z.L. Wu and S.Y. Wu, Characterizations of the solution sets of convex programs and variational inequality problems, J. Optim. Theory Appl., 130 (2006), 339-358.
  17. K.Q. Zhao and X.M. Yang, Characterizations of the solution set for a class of nonsmooth optimization problems, Optim. Lett., 7 (2013), 685-694. https://doi.org/10.1007/s11590-012-0471-y