The present invention provides an algorithm that does not relax the problem at the very onset, even if x.sub.f is infeasible. Instead, it solves the EQP with the initial guess for the active set without relaxing the problem. If this solution to the first EQP is not optimal, but nevertheless feasible, we can use this as our guess for the feasible point. This has the advantage of being a feasible point that is consistent with the initial active set, whereas the initial guess used in the previous method is not necessarily so.