Variational Analysis (Grundlehren der mathematischen Wissenschaften, 317) by R. Tyrrell Rockafellar (PDF)

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. 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.

User’s Reviews

Editorial Reviews: From the Back Cover 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 Author 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A winner of the prestigious Lanchester prize in 1997 (the very year it was published), this book is an instant classic. Written by two eminent researchers in the field, it is a handy reference on convex analysis, duality, optimality conditions, set-valued mappings, epigraphical convergence and variational problems.Resulting analysis is applicable to a wide variety of problems in mathematical optimization, operations research, management science, economics and engineering. New and unpublished structural results have been derived in this book and presented in the light of new developments in this area. To give an example, “Variational Analysis” advances some of the results in the princeton classic “Convex Analysis” (an almost necessary read for any researcher in mathematical optimization) also written by the first author of this book. To my knowledge, there is no other book at this time which compiles all the results in this area under one hood.The book follows a theorem-proof format for most part. Thus, it serves more as a reference than a textbook. A complete reading would be daunting given the length and density of material in the text.This book is worth buying if you are a researcher in mathematical optimization. To quote the citation of the Lanchester award:”In all, this book should serve as a landmark in the technical progress of optimization, an essential technical tool of operations research and the management sciences.”

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