  Metric regularity has emerged during last 2-3 decades as one of the central
concepts of variational analysis. The roots of this concept go back to a circle
of fundamental regularity ideas of classical analysis embodied in such results
as the implicit function theorem, Banach open mapping theorem, theorems of
Lyusternik and Graves, on the one hand, and the Sard theorem and the Thom-Smale
transversality theory, on the other. The three principal themes that are in the
focus of attention are: (a) regularity criteria (containing quantitative
estimates for rates of regularity) including formal comparisons of their
relative power and precision; (b) stability problems relating to the effect of
perturbations of the mapping on its regularity properties, on the one hand, and
to solutions of equations, inclusions etc. on the other; (c) role of metric
regularity in analysis and optimization. All of them are studied at three
levels of generality: the general theory for (set-valued) mappings between
metric spaces is followed by a detailed study of Banach and finite dimensional
theories. There is a number of new results, both theoretical and relating to
applications, and some known results are supplied with new, usually simpler,
proofs.

Optimization and Control