cover design

Nonsmooth Mechanics and Convex Optimization

Yoshihiro Kanno

CRC Press (2011)

Table of contents
Product details
Errata and supplements
Related talks
Catalog links
Bibtex entry

Table of contents

  1. Convex Optimization over Symmetric Cone
    1. Cones, Complementarity, and Conic Optimization
    2. Optimality and Duality
    3. Applications in Structural Engineering
  2. Cable Networks: An Example in Nonsmooth Mechanics
    1. Principles of Potential Energy for Cable Networks
    2. Duality in Cable Networks: Principles of Complementary Energy
  3. Numerical Methods
    1. Algorithms for Conic Optimization
    2. Numerical Analysis of Cable Networks
  4. Problems in Nonsmooth Mechanics
    1. Masonry Structures
    2. Planar Membranes
    3. Frictional Contact Problems
    4. Plasticity
Detailed table of contents

Product details

Hardcover: 425 pages (plus xx pages)
Publisher: CRC press (April 1, 2011)
ISBN-13: 9781420094237
ISBN-10: 1420094238

Errata and supplements


“This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality; non-smooth analysis; linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts and woven them into a seamless whole, by retaining an easy consistent style throughout. The book is not all theory: there are many real-life applications in structural engineering, cable networks, frictional contact problems and plasticity...... I recommend it to any reader who desires a modern, authoritative account of non-smooth mechanics and convex optimization.”

— Prof. Graham M.L. Gladwell
Distinguished Professor Emeritus, University of Waterloo,
Fellow of the Royal Society of Canada

The book “reads very well—the structure is good, the language and style are clear and fluent, and the material is rendered accessible by a careful presentation which contains many concrete examples. The range of applications, particularly to problems in mechanics, is admirable and a valuable complement to theoretical and computational investigations that are at the forefront of the areas concerned.”

— Prof. B. Daya Reddy
Department of Mathematics and Applied Mathematics,
Director of Centre for Research in Computational and Applied Mechanics,
University of Cape Town

“Many materials and structures (e.g., cable networks, membrane) involved in practical engineering applications have complex responses, which cannot be described by smooth constitutive relations. In the present book, the author shows that how these difficult problems can be tackled in the framework of convex analysis by arranging the carefully chosen materials in an elegant way. Most of the contents of the book are from the original contributions of the author. They are both mathematically rigorous and readable. This book is a must read for anyone who intends to get an authoritative and state-of-art description for the analysis of nonsmooth mechanics problems with theory and tools from convex analysis.”

— Prof. Xu Guo
State Key Laboratory of Structural Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology


  1. Review by Prof. Stanisław Migórski (Jagiellonian University) on MathSciNet (MR2797036 (2012h:90003)):
    “The book is of particular interest to mechanicians. It also provides motivations for applied mathematicians who are invited by this book to treat the nonsmooth properties of mechanics problems. In this respect, the book reminds me of the fact that the first lecture that Stefan Banach gave at the Jagiellonian University in Krakow, Poland was not on mathematics but on continuum mechanics...... The text is rather self-contained with a clear structure, the material is presented nicely which makes it accessible to young researchers, the style is fluent and the examples are carefully selected. The monograph confirms the existence of strong interaction between mechanics and applied mathematics. It will certainly acquire an important position in everybody's Mechanics and Applied Mathematics library.”

Related talks

  1. Talk on “topology optimization of tensegrity structures based on nonsmooth mechanics” given at ACOMEN 2011, November 2011 (PDF file)
  2. Japanese Talk on “SOCP formulation for von Mises plasticity” given at the 2011 Annual Conference of the JSIAM (PDF file)
  3. Abstract in Japanese for the talk on “”ρŠŠ—ΝŠw‚ƍœK‰»‚̐”—” given at R2P/IST‹Zpΰ–Ύ‰ο (“Œ‹ž‘εŠw‘εŠw‰@ξ•ρ—HŠwŒnŒ€‹†‰Θ), February 2011 (abstract)
  4. Talk on “duality in cable networks” given at CJK-OSM2, November 2002 (PDF file)

Catalog links

Bibtex entry


    author = "Yoshihiro Kanno",

    title = "Nonsmooth Mechanics and Convex Optimization",

    publisher = "CRC Press",

    address = "Boca Raton",

    year = "2011"}