TABLE OF CONTENTS The concept of a robust counterpart of an optimization problem with uncertain data (see section 3.4.2) is in no sense restricted to LP. Whenever we have an optimization problem depending on certain data, we may ask what happens when the data are uncertain and all we know is an uncertainty set the data belong to. Given such an uncertainty set, we may require candidate solutions to be robust feasible-to satisfy the realizations of the constraints for all data belonging through the uncertainty set. The robust counterpart of an uncertain problem is the problem of minimizing the objective [31] over the set of robust feasible solutions.
Now, we have seen in section 3.4.2 that the robust form of an uncertain linear inequality with the coefficients varying in an ellipsoid is a conic quadratic inequality; as a result, the robust counterpart of an uncertain LP problem with ellipsoidal uncertainty is a conic quadratic problem. What is the robust form of an uncertain CQI
with uncertain data 
? We want to know how to describe the set of all robust feasible solutions of this inequality, i.e., the set of x ?s such that
We are about to demonstrate that in the case when the data ( P, p) of the left-hand side and the data ( q, r) of the right-hand side of the inequality (4.5.58) independently of each other run through respective ellipsoids, i.e., the uncertainty set is of the form
then...
