NonSmooth Analysis - Giải tích không trơn

One of the sources of the classical differential calculus is the search for minimumor maximum points of a real-valued function. Similarly, nonsmoothanalysis originates in extremum problems with nondifferentiable data. By now,a broad spectrum of refined concepts and methods modeled on the theory ofdifferentiation has been developed.non-smoothThe idea underlying the presentation of the material in this book is to startwith simple problems treating them with simple methods, gradually passingto more difficult problems which need more sophisticated methods. In thissense, we pass from convex functionals via locally Lipschitz continuous functionalsto general lower semicontinuous functionals. The book does not aimat being comprehensive but it presents a rather broad spectrum of importantand applicable results of nonsmooth analysis in normed vector spaces. Eachchapter ends with references to the literature and with various exercises.The book grew out of a graduate course that I repeatedly held at the TechnischeUniversität Dresden. Susanne Walther and Konrad Groh, participantsof one of the courses, pointed out misprints in an early script preceding thebook. I am particularly grateful to Heidrun P¨uhl and Hans-Peter Scheffler fora time of prolific cooperation and to the latter also for permanent technicalsupport. The Institut f¨ur Analysis of the Technische Universit¨at Dresden providedme with the facilities to write the book. I thank Quji J. Zhu for usefuldiscussions and two anonymous referees for valuable suggestions. I gratefullyacknowledge the kind cooperation of Springer, in particular the patient supportby Stefanie Zoeller, as well as the careful work of Nandini Loganathan,project manager of Spi (India).

Dresden, December 2006 Winfried Schirotzek

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