Alexander Y. Kruger The paper concerns the computation of the graphical derivative and the regular (Frechet) coderivative of the solution map to a class of generalized equations, where the multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by C2 inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, … Read more
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects — slopes — are introduced and a classification scheme of error bound criteria is presented. Citation Published in Vietnam … Read more
This article investigates extremality, stationarity, and regularity properties of infinite collections of sets in Banach spaces. Our approach strongly relies on the machinery developed for finite collections. When dealing with an infinite collection of sets, we examine the behaviour of its finite subcollections. This allows us to establish certain primal-dual relationships between the stationarity/regularity properties … Read more
This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger & L�pez (2012) and is mainly focused on the application of the criteria from Kruger & L�pez (2012) to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly … Read more
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented. Citation Published in Nonlinear Analysis. … Read more
We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be derived. Our most abstract models are (multi-) functions on complete metric spaces. … Read more
This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems … Read more
In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its “small” perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error … Read more
Stationarity and regularity concepts for the three typical for variational analysis classes of objects — real-valued functions, collections of sets, and multifunctions — are investigated. An attempt is maid to present a classification scheme for such concepts and to show that properties introduced for objects from different classes can be treated in a similar way. … Read more
The paper presents a general classiffication scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. Citation Published in Set-Valued and … Read more