First-order conditions for isolated locally optimal solutions

There are well-known first-order sufficient conditions for a pointx ₀ to be a strict locally optimal solution of a nonlinear programming problem. In this paper, we show that these conditions also guarantee thatx ₀ is an isolated stationary point of the considered program provided a constraint qualification holds. This result has an interesting application to finite convergence of algorithms along the lines suggested by Al-Khayyal and Kyparisis.This research was supported in part by National Science Foundation Grant DDM-91-14489.