Approximate subgradients and coderivatives in R
n |
| |
Authors: | D Borwein J M Borwein Xianfu Wang |
| |
Institution: | 1. Department of Mathematics, University of Western Ontario, N6A 5B7, London, Ontario, Canada 2. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, BC, Canada 3. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, BC, Canada
|
| |
Abstract: | We show that in two dimensions or higher, the Mordukhovich-Ioffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Fréchet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be nonconvex almost everywhere for Fréchet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|