Convexity and Well-Posed Problems

  • Roberto Lucchetti

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Roberto Lucchetti
    Pages 21-30
  3. Roberto Lucchetti
    Pages 31-54
  4. Roberto Lucchetti
    Pages 55-77
  5. Roberto Lucchetti
    Pages 79-97
  6. Roberto Lucchetti
    Pages 99-116
  7. Roberto Lucchetti
    Pages 117-137
  8. Roberto Lucchetti
    Pages 139-167
  9. Roberto Lucchetti
    Pages 169-183
  10. Roberto Lucchetti
    Pages 185-217
  11. Roberto Lucchetti
    Pages 219-248
  12. Roberto Lucchetti
    Pages 249-256
  13. Back Matter
    Pages 257-305

About this book

Introduction

Intended for graduate students especially in mathematics, physics, and

economics, this book deals with the study of convex functions and of

their behavior from the point of view of stability with respect to

perturbations. The primary goal is the study of the problems of

stability and well-posedness, in the convex case. Stability means the

basic parameters of a minimum problem do not vary much if we slightly

change the initial data. Well-posedness means that points with values

close to the value of the problem must be close to actual solutions.

In studying this, one is naturally led to consider perturbations of

both functions and of sets.

The book includes a discussion of numerous topics, including:

* hypertopologies, ie, topologies on the closed subsets of a metric space;

* duality in linear programming problems, via cooperative game theory;

* the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions;

* questions related to convergence of sets of nets;

* genericity and porosity results;

* algorithms for minimizing a convex function.

In order to facilitate use as a textbook, the author has included a

selection of examples and exercises, varying in degree of difficulty.

Robert Lucchetti is Professor of Mathematics at Politecnico di Milano. He has taught this material to graduate students at his own university, as well as the Catholic University of Brescia, and the University of Pavia.

Keywords

Convexity calculus derivative differential equation functional analysis game theory linear optimization minimum optimization

Authors and affiliations

  • Roberto Lucchetti
    • 1
  1. 1.Dipto. MatematicaPolitecnico di MilanoMilanoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-31082-7
  • Copyright Information Springer-Verlag New York 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-28719-5
  • Online ISBN 978-0-387-31082-4
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • About this book