Book reviews" "Boris S. Mordukhovich; Variational Analysis and Applications", Springer Monographs in Mathematics. Springer, Cham, 2018. xix+622 p. ISBN: 978-3-319-92773-2/hbk; 978-3-319-92775-6/ebook.

Abstract

Although variational principles in mathematical physics and mechanics were known since the 18th century, variational analysis, in its current acceptance, is a relatively new discipline. Its aim is to treat optimization and control problems via perturbations, approximations and generalized differentiation of nonsmooth or set- valued maps. As the author mentions in Preface, the first monograph dedicated to variational analysis in finite dimensions is that by R. T. Rockafellar and R. J.B. Wets, Springer 1998, where this very name was coined. The infinite-dimensional case is treated at large in the impressive two-volume monograph of the author, Variational analysis and generalized differentiation. I: Basic theory (579 p), II: Applications (610 p), Springer 2006 (a review of these volumes is published in vol. 52 (2007), no. 1, of the present journal).