Calculus without derivatives / Jean-Paul Penot

Auteur: Penot, Jean-Paul (1942-) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 266Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, cop. 2013Description: 1 vol. (XX-524 p.) ; 24 cm ISBN: 9781461445371 ; rel. Résumé: Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis. (Source : Springer).Bibliographie: Bibliogr. p. 479-517. Index. Sujets MSC: 49J52 Calculus of variations and optimal control; optimization -- Existence theories -- Nonsmooth analysis
49J53 Calculus of variations and optimal control; optimization -- Existence theories -- Set-valued and variational analysis
58C20 Global analysis, analysis on manifolds -- Calculus on manifolds; nonlinear operators -- Differentiation theory (Gateaux, Fréchet, etc.)
54C60 General topology -- Maps and general types of spaces defined by maps -- Set-valued maps
52A41 Convex and discrete geometry -- General convexity -- Convex functions and convex programs
90C30 Operations research, mathematical programming -- Mathematical programming -- Nonlinear programming
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Bibliogr. p. 479-517. Index

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis. (Source : Springer)

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