Stationarity results for generating set search for linearly constrained optimization.

We derive new stationarity results for derivative-free, generating set search methods for linearly constrained optimization. We show that a particular measure of stationarity is of the same order as the step length at an identifiable subset of the iterations. Thus, even in the absence of explicit knowledge of the derivatives of the objective function, we still have information about stationarity. These results help both unify the convergence analysis of several classes of direct search algorithms and clarify the fundamental geometrical ideas that underlie them. In addition, these results validate a practical stopping criterion for such algorithms