Preface

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 from classical analysis embodied in such results as the implicit function theorem, the Banach open mapping theorem, and theorems of Lyusternik and Graves, on the one hand, and Sard’s theorem and transversality theory, on the other hand. Smoothness is the key property of the objects to which the classical results are applied. Variational analysis, on the other hand, appeals to objects that may lack this property: functions and maps that are nondifferentiable at points of interest, set-valued mappings, etc. Such phenomena naturally appear in optimization theory and elsewhere. In traditional nonlinear analysis, regularity of a continuously differentiable mapping (e.g., from a normed space or a manifold to another space or manifold) at a certain point means that its derivative at the point is an operator onto. This property, translated through available analytic or topological means to corresponding local