Advertisement

Quasiconvex Optimization and Location Theory

  • Jaoquim António dos Santos Gromicho

Part of the Applied Optimization book series (APOP, volume 9)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Jaoquim António dos Santos Gromicho
    Pages 1-4
  3. Jaoquim António dos Santos Gromicho
    Pages 5-32
  4. Jaoquim António dos Santos Gromicho
    Pages 33-78
  5. Jaoquim António dos Santos Gromicho
    Pages 79-123
  6. Jaoquim António dos Santos Gromicho
    Pages 125-181
  7. Jaoquim António dos Santos Gromicho
    Pages 183-196
  8. Jaoquim António dos Santos Gromicho
    Pages 197-197
  9. Back Matter
    Pages 199-218

About this book

Introduction

grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro­ grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C­ programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com­ positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.

Keywords

algorithms classification complexity computation derivative derivatives dynamic programming Facility Location geometry optimization programming sets Subdifferential

Authors and affiliations

  • Jaoquim António dos Santos Gromicho
    • 1
  1. 1.GoudaThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-3326-5
  • Copyright Information Springer-Verlag US 1998
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-3328-9
  • Online ISBN 978-1-4613-3326-5
  • Series Print ISSN 1384-6485
  • Buy this book on publisher's site