Variational Analysis - R. Tyrrell Rockafellar, Roger J.-B. Wets

Variational Analysis

Buch | Softcover
XII, 736 Seiten
2010 | 1. Softcover reprint of hardcover 1st ed. 1998
Springer Berlin (Verlag)
978-3-642-08304-4 (ISBN)
181,89 inkl. MwSt
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.

From its origins in the minimization of integral functionals, the notion of 'variations' has evolved greatly in connection with applications in optimization, equilibrium, and control. It refers not only to constrained movement away from a point, but also to modes of perturbation and approximation that are best describable by 'set convergence', variational convergence of functions and the like. This book develops a unified framework and, in finite dimension, provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, maximal monotone mappings, second-order subderivatives, measurable selections and normal integrands.

The changes in this 3rd printing mainly concern various typographical corrections, and reference omissions that came to light in the previous printings. Many of these reached the authors' notice through their own re-reading, that of their students and a number of colleagues mentioned in the Preface. The authors also included a few telling examples as well as improved a few statements, with slightly weaker assumptions or have strengthened the conclusions in a couple of instances.

Both authors have long worked with applications of convex, and later nonconvex, analysis to problems in optimization. Both are recipients of the Dantzig Prize (awarded by SIAM and the Mathematical Programming Society): Rockafellar in 1982 and Wets in 1994.

Max and Min.- Convexity.- Cones and Cosmic Closure.- Set Convergence.- Set-Valued Mappings.- Variational Geometry.- Epigraphical Limits.- Subderivatives and Subgradients.- Lipschitzian Properties.- Subdifferential Calculus.- Dualization.- Monotone Mappings.- Second-Order Theory.- Measurability.

Erscheint lt. Verlag 1.12.2010
Reihe/Serie Grundlehren der mathematischen Wissenschaften
Illustrationen Maria Wets
Zusatzinfo XII, 736 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 1084 g
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Schlagworte Convex Analysis • epi-convergence • non-smooth analysis • Optimization • variational analysis
ISBN-10 3-642-08304-8 / 3642083048
ISBN-13 978-3-642-08304-4 / 9783642083044
Zustand Neuware
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