Second-order Sufficiency and Quadratic Growth for Nonisolated Minima

For standard nonlinear programming problems, the weak second-order sufficient condition is equivalent to the quadratic growth condition as far as the set of minima consists of isolated points and some qualification hypothesis holds. This kind of condition is instrumental in the study of numerical algorithms and sensitivity analysis. The arm of the paper is to study the relations between various types of sufficient conditions and quadratic growth in cases when the set of minima may have nonisolated points.