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Quasidifferentiability and Related Topics

  • Vladimir Demyanov
  • Alexander Rubinov

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 43)

Table of contents

  1. Front Matter
    Pages i-xix
  2. V. F. Demyanov, A. M. Rubinov
    Pages 1-31
  3. Ljudmila N. Polyakova, Georgios E. Stavroulakis
    Pages 215-233
  4. A. M. Rubinov
    Pages 235-261
  5. Li-Wei Zhang, Zun-Quan Xia
    Pages 329-359
  6. Back Matter
    Pages 393-395

About this book

Introduction

2 Radiant sets 236 3 Co-radiant sets 239 4 Radiative and co-radiative sets 241 5 Radiant sets with Lipschitz continuous Minkowski gauges 245 6 Star-shaped sets and their kernels 249 7 Separation 251 8 Abstract convex star-shaped sets 255 References 260 11 DIFFERENCES OF CONVEX COMPACTA AND METRIC SPACES OF CON- 263 VEX COMPACTA WITH APPLICATIONS: A SURVEY A. M. Rubinov, A. A. Vladimirov 1 Introduction 264 2 Preliminaries 264 3 Differences of convex compact sets: general approach 266 4 Metric projections and corresponding differences (one-dimensional case) 267 5 The *-difference 269 6 The Demyanov difference 271 7 Geometric and inductive definitions of the D-difference 273 8 Applications to DC and quasidifferentiable functions 276 9 Differences of pairs of set-valued mappings with applications to quasidiff- entiability 278 10 Applications to approximate subdifferentials 280 11 Applications to the approximation of linear set-valued mappings 281 12 The Demyanov metric 282 13 The Bartels-Pallaschke metric 284 14 Hierarchy of the three norms on Qn 285 15 Derivatives 287 16 Distances from convex polyhedra and convergence of convex polyhedra 289 17 Normality of convex sets 290 18 D-regular sets 291 19 Variable D-regular sets 292 20 Optimization 293 References 294 12 CONVEX APPROXIMATORS.

Keywords

algorithm analysis mathematical modeling mathematical programming modeling numerical methods optimization programming

Editors and affiliations

  • Vladimir Demyanov
    • 1
  • Alexander Rubinov
    • 2
  1. 1.Department of Applied MathematicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.School of Information Technology and Mathematical SciencesUniversity of BallaratAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3137-8
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4830-4
  • Online ISBN 978-1-4757-3137-8
  • Series Print ISSN 1571-568X
  • Buy this book on publisher's site