Linear Stability of Generalized Equations, Part II: Applications to Nonlinear Programming

(Dedicated to Anthony V. Fiacco on the occasion of his 65th birthday.)

We present an approach by which the quantitative stability of solutions of a general nonlinear programming problem is obtained in the spirit of Part I of the paper. Under assumptions of the constraint regularity and the general second-order sufficient condition. we show that the solution set is linearly stable under small allowed perturbations in the sense of Part I of the paper, and derive bounds for the linear stability number which characterizes the quantitative stability of solutions of the problem in question. For standard nonlinear programs that are most commonly encountered in practical situations, we develop a method to compute these bounds. The results obtained here complement those of Robinson (1982).