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 both viewpoints of optimization theory and its applications. Based on secondorder generalized differential tools of variational analysis, we obtain necessary and sufficient conditions for fully stable local minimizers in general classes of constrained optimization problems including problems of composite optimization, mathematical 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 subdifferentials, parametric proxregularity and amenability AMS subject classifications. 49J52, 90C30, 90C31 Abbreviated title. Full stability in optimization

The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems including those of conic and specifically semidefinite programming. Developing a new technique of variational analysis and generalized differentiation, we derive second-order characterizations of full stability, in both Lipschitzian and Hölderian settings, and establish their relationships with the conventional notions of strong regularity and strong stability for a large class of problems of constrained optimization with twice continuously differentiable data.

Abstract. This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefiniteness properties of the second-order subdifferential (or generalized Hessian). Key words. variational analysis, quadratic growth, first-order and second-order generalized differentiation, metric regularity and subregularity, prox-regular functions, tilt stability in optimization AMS subject classifications. 49J52, 49J53, 90C31 1