© 1998

Variational Analysis


  • Includes corrections, some simplifications and some additional comments


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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-37
  3. Pages 38-76
  4. Pages 108-147
  5. Pages 148-195
  6. Pages 196-237
  7. Pages 238-297
  8. Pages 349-420
  9. Pages 421-472
  10. Pages 473-532
  11. Pages 533-578
  12. Pages 579-641
  13. 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.


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

Authors and affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA

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

  • Book Title Variational Analysis
  • Authors R. Tyrrell Rockafellar
    Roger J.-B. Wets
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-62772-2
  • Softcover ISBN 978-3-642-08304-4
  • eBook ISBN 978-3-642-02431-3
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XII, 736
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Calculus of Variations and Optimal Control; Optimization
    Systems Theory, Control
  • Buy this book on publisher's site