Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
linear fractional program; robust optimization; uncertainty; second order cone
linear fractional program; robust optimization; uncertainty; second order cone
Summary:
In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional program, however under ellipsoidal uncertainty it is equivalent to a linear fractional program with both linear and second order cone constraints. In addition, for each case we have studied the dual problems associated with the robust counterparts. It is shown that in both cases, either interval or ellipsoidal uncertainty, the dual of robust counterpart is equal to the optimistic counterpart of dual problem.
References:
[1] Beck, A., Ben-Tal, A.: Duality in robust optimization: primal worst equals dual best. Oper. Res. Lett. 37 (2009), 1-6. DOI 10.1016/j.orl.2008.09.010 | MR 2488072 | Zbl 1154.90614
[2] Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88 (2000), 411-424. DOI 10.1007/PL00011380 | MR 1782149 | Zbl 0964.90025
[3] Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25 (1999), 1-13. DOI 10.1016/S0167-6377(99)00016-4 | MR 1702364 | Zbl 1089.90037
[4] Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23 (1998), 769-805. DOI 10.1287/moor.23.4.769 | MR 1662410 | Zbl 1135.90046
[5] Charnes, A., Cooper, W. W.: Programming with linear fractional functional. Naval Res. Logist. Quart. 9 (1962), 181-186. DOI 10.1002/nav.3800090303 | MR 0152370
[6] Chinchuluun, A., Yuan, D., Pardalos, P. M: Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity. Ann. Oper. Res. 154 (2007), 133-147. DOI 10.1007/s10479-007-0180-6 | MR 2332825 | Zbl 1191.90080
[7] Bertsimas, D., Pachamanova, D., Sim, M.: Robust linear optimization under general norms. Oper. Res. Lett. 32 (2004), 510-516. DOI 10.1016/j.orl.2003.12.007 | MR 2077451 | Zbl 1054.90046
[8] Bitran, G. R., Novaes, A. J.: Linear programming with a fractional objective function. Oper. Res. 21 (1973), 22-29. DOI 10.1287/opre.21.1.22 | MR 0368741 | Zbl 0259.90046
[9] Pardalos, P. M., Phillips, A.: Global optimization of fractional programs. J. Global Optim. 1 (1991), 173-182. DOI 10.1007/BF00119990 | MR 1263589 | Zbl 0748.90068
[10] Schaible, S.: Fractional programming a recent survey, Generalized convexity, generalized monotonicity, optimality conditions and duality in scalar and vector optimization. J. Statist. Management Syst. 5 (2002), 63-86. MR 1993086
[11] Schaible, S.: Parameter-free convex equivalent and dual programs of fractional programming problems. Oper. Res. 18 (1974), 187-196. MR 0351464 | Zbl 0291.90067
[12] Gómez, T., Hernández, M., León, M. A., Caballero, R.: A forest planning problem solved via a linear fractional goal programming model. Forest Ecol. Management 227 (2006), 79-88.
[13] Jeyakumar, V., Li, G. Y.: Robust duality for fractional programming problems with constraint-wise data uncertainty. J. Optim. Theory Appl. 151 (2011), 292-303. DOI 10.1007/s10957-011-9896-1 | MR 2852402 | Zbl 1242.90252
Search
Partner of
