CHARACTERIZATIONS OF FULL STABILITY IN CONSTRAINED OPTIMIZATION∗

Abstract. This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from the viewpoints of both optimization theory and its applications. Based on second-order generalized differential tools of variational anal-ysis, we obtain necessary and sufficient conditions for fully stable local minimizers in general classes of constrained optimization problems, including problems of composite optimization, mathemati-cal programs with polyhedral constraints, as well as problems of extended and classical nonlinear programming with twice continuously differentiable data. Key words. variational analysis, constrained parametric optimization, nonlinear and extended nonlinear programming, full stability of local minimizers, strong regularity, second-order subdiffer-entials, parametric prox-regularity, amenabilit