Linear stability of generalized equations, Part II: Applications to nonlinear programming

The paper presents 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, it shows that the solution set is linearly stable under small allowed perturbations in the sense of Part I of the paper, and derives 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, the paper develops a method to compute these bounds. The results obtained here complement those of Robinson.