Overview

A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions. No other recent monograph in nonsmooth analysis is devoted to vector-valued maps, a growing area of research. Illustrated by numerous examples of known generalized derivatives, the work serves as a valuable reference for graduate students, researchers, and applied mathematicians who wish to use nonsmooth techniques and continuous optimization to model and solve problems in mathematical programming, operations research, and engineering. Readers require only a modest background in undergraduate mathematical analysis.