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＜電子ブック＞
Variational Analysis / by R. Tyrrell Rockafellar, Roger J.-B. Wets
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 317)

版	1st ed. 1998.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1998
本文言語	英語
大きさ	XII, 736 p : online resource
著者標目	*Rockafellar, R. Tyrrell author Wets, Roger J.-B author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:System theory LCSH:Control theory FREE:Calculus of Variations and Optimization FREE:Systems Theory, Control
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-02431-3

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