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Variational Analysis
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  • Title Variational Analysis
  • Author(s) R. Tyrrell Rockafellar, Roger J-B Wets
  • Publisher: Springer (December 1, 2010); eBook (Final Draft, 3rd Printing 2009)
  • Paperback 748 pages
  • eBook PDF (743 pages, 5.4 MB)
  • Language: English
  • ISBN-10: 3642083048
  • ISBN-13: 978-3642083044
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Book Description

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.

About the Authors
  • R. Tyrrell Rockafellar is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics.
  • Roger J-B Wets is a "pioneer" in stochastic programming and a leader in variational analysis.
  • 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.
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