Linear fractional program under interval and ellipsoidal uncertainty

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