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  • Book
  • © 1998

Variational Analysis

  • Includes corrections, some simplifications and some additional comments

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 317)

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  • ISBN: 978-3-642-02431-3
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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xi
  2. Max and Min

    Pages 1-37
  3. Convexity

    Pages 38-76
  4. Set Convergence

    Pages 108-147
  5. Set-Valued Mappings

    Pages 148-195
  6. Variational Geometry

    Pages 196-237
  7. Epigraphical Limits

    Pages 238-297
  8. Lipschitzian Properties

    Pages 349-420
  9. Subdifferential Calculus

    Pages 421-472
  10. Dualization

    Pages 473-532
  11. Monotone Mappings

    Pages 533-578
  12. Second-Order Theory

    Pages 579-641
  13. Measurability

    Pages 642-683
  14. Back Matter

    Pages 684-734

About this book

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.

Keywords

  • convex analysis
  • epi-convergence
  • non-smooth analysis
  • optimization
  • variational analysis

Authors and Affiliations

  • Department of Mathematics, University of Washington, Seattle, USA

    R. Tyrrell Rockafellar

  • Department of Mathematics, University of California at Davis, Davis, USA

    Roger J. B. Wets

About the authors

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.

Bibliographic Information

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-02431-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 199.99
Price excludes VAT (USA)
Hardcover Book USD 199.99
Price excludes VAT (USA)