Document Type

Technical Report


The primary goal of this paper is to study some notions of normals to nonconvex sets in finite-dimensional and infinite-dimensional spaces and their images under single-valued and set-valued mappings. The main motivation for our study comes from variational analysis and optimization, where the problems under consideration play a crucial role in many important aspects of generalized differential calculus and applications. Our major results provide precise equality formulas (sometimes just efficient upper estimates) allowing us to compute generalized normals in various senses to direct and inverse images of nonconvex sets under single-valued and set-valued mappings between Banach spaces. The main tools of our analysis revolve around variational principles and the fundamental concept of metric regularity properly modified in this paper.

Number in Series



Applied Mathematics | Mathematics

AMS Subject Classification

Primary 49J52, 49J53; Secondary 46B20, 58C20, 90C31.


Dedicated to Alex Ioffe in honor of his 70th birthday. This research was partially supported by the National Science Foundation under grant DMS-0603846.