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Quasidifferentiability and Related Topics

  • Book
  • © 2000

Overview

Editors:
  1. Vladimir Demyanov

    1. Department of Applied Mathematics, St. Petersburg State University, St. Petersburg, Russia

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    You can also search for this editor in PubMed   Google Scholar

  2. Alexander Rubinov

    1. School of Information Technology and Mathematical Sciences, University of Ballarat, Australia

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xix
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  2. An Introduction to Quasidifferential Calculus

    • V. F. Demyanov, A. M. Rubinov
    Pages 1-31

  3. Numerical Methods for Minimizing Quasidifferentiable Functions: A Survey and Comparison

    • Adil M. Bagirov
    Pages 33-71

  4. Dual Representations of Classes of Positively Homogeneous Functions

    • Marco Castellani
    Pages 73-84

  5. Exhausters and Convexificators — New Tools in Nonsmooth Analysis

    • V. F. Demyanov
    Pages 85-137

  6. On Directional Differentiability of Marginal Functions in Quasidifferentiable Case

    • Sergey I. Dudov
    Pages 139-149

  7. Optimality Conditions with Lagrange Multipliers for Inequality Constrained Quasidifferentiable Optimization

    • Yan Gao
    Pages 151-162

  8. Strongly Differentiable Multifunctions and Directional Differentiability of Marginal Functions

    • L. Minchenko, A. Volosevich
    Pages 163-171

  9. Minimal Pairs of Compact Convex Sets, with Application to Quasidifferential Calculus

    • Diethard Pallaschke, Ryszard UrbaÅ„ski
    Pages 173-213

  10. QD and DC Optimization for Pseudoelastic Modeling of Shape Memory Alloys

    • Ljudmila N. Polyakova, Georgios E. Stavroulakis
    Pages 215-233

  11. Radiant Sets and Their Gauges

    • A. M. Rubinov
    Pages 235-261

  12. Differences of Convex Compacta and Metric Spaces of Convex Compacta with Applications: A Survey

    • A. M. Rubinov, A. A. Vladimirov
    Pages 263-296

  13. Convex Approximators, Convexificators and Exhausters: Applications to Constrained Extremum Problems

    • Amos Uderzo
    Pages 297-327

  14. Approximations to Convex-Valued Multifunctions

    • Li-Wei Zhang, Zun-Quan Xia
    Pages 329-359

  15. Continuous Approximations, Codifferentiable Functions and Minimization Methods

    • Alberto Zaffaroni
    Pages 361-391

  16. Back Matter

    Pages 393-395
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Applied Mathematics, St. Petersburg State University, St. Petersburg, Russia

    Vladimir Demyanov

  • School of Information Technology and Mathematical Sciences, University of Ballarat, Australia

    Alexander Rubinov

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