© 1998

Convex Analysis and Global Optimization


Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 22)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Convex Analysis

    1. Front Matter
      Pages 1-1
    2. Hoang Tuy
      Pages 3-40
    3. Hoang Tuy
      Pages 41-81
    4. Hoang Tuy
      Pages 83-105
  3. Global Optimization

    1. Front Matter
      Pages 107-107
    2. Hoang Tuy
      Pages 109-132
    3. Hoang Tuy
      Pages 133-176
    4. Hoang Tuy
      Pages 177-222
    5. Hoang Tuy
      Pages 223-276
    6. Hoang Tuy
      Pages 277-318
  4. Back Matter
    Pages 319-339

About this book


Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development.
Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.


Approximation Mathematica Partition calculus computer computer science global optimization operations research optimization programming

Authors and affiliations

  1. 1.Institute of MathematicsHanoiVietnam

Bibliographic information


`The book gives a good review of the topic. ... The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.'
Mathematical Methods of Operations Research, 49:3 (1999)