change problem lp;
CPXchgprobtype().
You can then solve the relaxed linear version by means of the ILOG CPLEX primal simplex optimizer. Then you can apply the ILOG CPLEX infeasibility finder to that relaxed solution, with its associated, original QP information, to help you diagnose the source of the infeasibility. (Diagnosing LP Infeasibility explains how to use the ILOG CPLEX infeasibility finder following a simplex optimizer.)
Just as our recommendation regarding numerical difficulties on LP models (see Numerical Difficulties) is for coefficients in the constraint matrix not to vary by more than about six orders of magnitude, for QP this recommendation expands to include the quadratic elements of the objective function coefficients as well. Fortunately, in most instances it is straightforward to scale your objective function, by multiplying or dividing all the coefficients (linear and quadratic) by a constant factor, which changes the unit of measurement for the objective but does not alter the meaning of the variables or the sense of the problem as a whole. If your objective function itself contains a wide variation of coefficient magnitudes, you may also want to consider scaling the individual columns to achieve a closer range.