Quasidifferentiability and Related Topics

ISBN-13: 9781441948304 / Angielski / Miękka / 2010 / 395 str.

Vladimir F. Demyanov; Alexander M. Rubinov

Opis

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.

Spis treści

Preface. References. 1. An Introduction to Quasidifferential Calculus; V.F. Demyanov, A.M. Rubinov. 2. Numerical Methods for Minimizing Quasidifferentiable Functions: A Survey and Comparison; A.M. Bagirov. 3. Dual Representations of Classes of Positively Homogeneous Functions; M. Castellani. 4. Exhausters and Convexificators - New Tools in Nonsmooth Analysis; V.F. Demyanov. 5. On Directional Differentiability of Marginal Functions in Quasidifferentiable Case; S.I. Dudov. 6. Optimality Conditions with Lagrange Multipliers for Inequality Constrained Quasidifferentiable Optimization; Y. Gao. 7. Strongly Differentiable Multifunctions and Directional Differentiability of Marginal Functions; L. Minchenko, A. Volosevich. 8. Minimal Pairs of Compact Convex Sets, with Application to Quasidifferential Calculus; D. Pallaschke, R. Urbanski. 9. QD and DC Optimization for Pseudoelastic Modeling of Shape Memory Alloys; L.N. Polyakova, G.E. Stavroulakis. 10. Radiant Sets and Their Gauges; A.M. Rubinov. 11. Differences of Convex Compacta and Metric Spaces of Convex Compacta with Applications: a Survey; A.M. Rubinov, A.A. Vladimirov. 12. Convex Approximators, Convexificators and Exhausters: Applications to Constrained Extremum Problems; A. Uderzo. 13. Approximations to Convex-Valued Multifunctions; L.-W. Zhang, Z.-Q. Xia. 14. Continuous Approximations, Codifferentiable Functions and Minimization Methods; A. Zaffaroni.