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© 1993

Convex Analysis and Minimization Algorithms I

Fundamentals

Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 305)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 1-46
  3. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 47-86
  4. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 87-141
  5. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 143-193
  6. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 195-236
  7. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 237-289
  8. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 291-341
  9. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
    Pages 343-384
  10. Back Matter
    Pages 385-420

About this book

Introduction

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

Keywords

Convex Analysis Mathematical Programming Nonsmooth Optimization Numerical Algorithms algorithms operations research optimization

Authors and affiliations

  1. 1.Département de MathématiquesUniversité Paul SabatierToulouseFrance
  2. 2.Rocquencourt, Domaine de VoluceauINRIALe ChesnayFrance

Bibliographic information

Reviews

From the reviews: "... The book is very well written, nicely illustrated, and clearly understandable even for senior undergraduate students of mathematics... Throughout the book, the authors carefully follow the recommendation by A. Einstein: 'Everything should be made as simple as possible, but not simpler.'"