Geodesic
Linear fractional program under interval and ellipsoidal uncertainty
Kybernetika, Tome 49 (2013) no. 1, pp. 181-187 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 90C05, 90C25, 90C32
Keywords: linear fractional program; robust optimization; uncertainty; second order cone 
@article{KYB_2013_49_1_a12,
     author = {Salahi, Maziar and Fallahi, Saeed},
     title = {Linear fractional program under interval and ellipsoidal uncertainty},
     journal = {Kybernetika},
     pages = {181--187},
     year = {2013},
     volume = {49},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_1_a12/}
}
TY  - JOUR
AU  - Salahi, Maziar
AU  - Fallahi, Saeed
TI  - Linear fractional program under interval and ellipsoidal uncertainty
JO  - Kybernetika
PY  - 2013
SP  - 181
EP  - 187
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_2013_49_1_a12/
LA  - en
ID  - KYB_2013_49_1_a12
ER  - 
%0 Journal Article
%A Salahi, Maziar
%A Fallahi, Saeed
%T Linear fractional program under interval and ellipsoidal uncertainty
%J Kybernetika
%D 2013
%P 181-187
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_2013_49_1_a12/
%G en
%F KYB_2013_49_1_a12
Salahi, Maziar; Fallahi, Saeed. Linear fractional program under interval and ellipsoidal uncertainty. Kybernetika, Tome 49 (2013) no. 1, pp. 181-187. http://geodesic.mathdoc.fr/item/KYB_2013_49_1_a12/

[1] Beck, A., Ben-Tal, A.: Duality in robust optimization: primal worst equals dual best. Oper. Res. Lett. 37 (2009), 1-6. | DOI | MR | Zbl

[2] Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88 (2000), 411-424. | DOI | MR | Zbl

[3] Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25 (1999), 1-13. | DOI | MR | Zbl

[4] Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23 (1998), 769-805. | DOI | MR | Zbl

[5] Charnes, A., Cooper, W. W.: Programming with linear fractional functional. Naval Res. Logist. Quart. 9 (1962), 181-186. | DOI | MR

[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 | MR | Zbl

[7] Bertsimas, D., Pachamanova, D., Sim, M.: Robust linear optimization under general norms. Oper. Res. Lett. 32 (2004), 510-516. | DOI | MR | Zbl

[8] Bitran, G. R., Novaes, A. J.: Linear programming with a fractional objective function. Oper. Res. 21 (1973), 22-29. | DOI | MR | Zbl

[9] Pardalos, P. M., Phillips, A.: Global optimization of fractional programs. J. Global Optim. 1 (1991), 173-182. | DOI | MR | Zbl

[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

[11] Schaible, S.: Parameter-free convex equivalent and dual programs of fractional programming problems. Oper. Res. 18 (1974), 187-196. | MR | Zbl

[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 | MR | Zbl