Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEM

  • Lee, Gue Myung (Department of Applied Mathematics Pukyong National University) ;
  • Lee, Jae Hyoung (Department of Applied Mathematics Pukyong National University)
  • Received : 2014.04.25
  • Accepted : 2014.06.30
  • Published : 2014.08.15
Download PDF
⟨ Previous Next ⟩

Abstract

A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.

Keywords

References

  1. A. Beck and A. Ben-Tal, Duality in robust optimization: primal worst equals dual best, Oper. Res. Lett. 37 (2009), 1-6. https://doi.org/10.1016/j.orl.2008.09.010
  2. F. Glover, A Multiphase-dual algorithm for the zero-one integer programming problem, Oper. Res. 13 (1965), 879-919. https://doi.org/10.1287/opre.13.6.879
  3. H. J. Greenberg, Quasi-conjugate functions and surrogate duality, Oper. Res. 21 (1973), 162-178. https://doi.org/10.1287/opre.21.1.162
  4. H. J. Greenberg and W. P. Pierskalla, Surrogate mathematical programming, Oper. Res. 18 (1970), 924-939. https://doi.org/10.1287/opre.18.5.924
  5. V. Jeyakumar, G. M. Lee, and N. Dinh, New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs, SIAM J. Optim. 20 (2003), 534-547.
  6. V. Jeyakumar and G. Y. Li, Strong duality in robust convex programming:complete characterizations, SIAM J. Optim. 20 (2010), 3384-3407. https://doi.org/10.1137/100791841
  7. G. Y. Li, V. Jeyakumar, and G. M. Lee, Robust conjugate duality for convex op-timization under uncertainty with application to data classification, Nonlinear Anal. 74 (2011), 2327-2341. https://doi.org/10.1016/j.na.2010.11.036
  8. D. G. Luenberger, Quasi-convex programming, SIAM J. Appl. Math. 16 (1968), 1090-1095. https://doi.org/10.1137/0116088
  9. J. P. Penot and M. Volle, On quasi-convex duality, Math. Oper. Res. 15 (1990), 597-625. https://doi.org/10.1287/moor.15.4.597
  10. J. P. Penot and M. Volle, Surrogate programming and multipliers in quasi-convex programming, SIAM J. Control Optim. 42 (2004), 1994-2003. https://doi.org/10.1137/S0363012902327819
  11. S. Suzuki and D. Kuroiwa, Necessary and sufficient constraint qualification for surrogate duality, J. Optim. Theory Appl. 152 (2012), 366-377. https://doi.org/10.1007/s10957-011-9893-4
  12. S. Suzuki, D. Kuroiwa, and G. M. Lee, Surrogate duality for robust optimiza-tion, European J. Oper. Res. 231 (2013), 257-262. https://doi.org/10.1016/j.ejor.2013.02.050