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Convex Analysis and Minimization Algorithms II

Advanced Theory and Bundle Methods

  • Book
  • © 1993

Overview

Authors:
  1. Jean-Baptiste Hiriart-Urruty

    1. Département de Mathématiques, Université Paul Sabatier, Toulouse, France

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    You can also search for this author in PubMed   Google Scholar

  2. Claude Lemaréchal

    1. INRIA, Rocquencourt, Domaine de Voluceau, Le Chesnay, France

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 306)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Inner Construction of the Subdifferential: Towards Implementing Descent Methods

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 1-34

  3. Conjugacy in Convex Analysis

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 35-90

  4. Approximate Subdifferentials of Convex Functions

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 91-136

  5. Abstract Duality for Practitioners

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 137-193

  6. Inner Construction of the Approximate Subdifferential: Methods of ε-Descent

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 195-222

  7. Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 223-274

  8. Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods

    • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 275-330

  9. Back Matter

    Pages 331-348
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About this book

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Reviews

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books. . . [is] that they are designed not for the expert, but for those who wish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Authors and Affiliations

  • Département de Mathématiques, Université Paul Sabatier, Toulouse, France

    Jean-Baptiste Hiriart-Urruty

  • INRIA, Rocquencourt, Domaine de Voluceau, Le Chesnay, France

    Claude Lemaréchal

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