Generalized subdifferentials: a Baire categorical approach
From MaRDI portal
Publication:2723455
DOI10.1090/S0002-9947-01-02820-3zbMath0979.49016OpenAlexW1600026779MaRDI QIDQ2723455
Jonathan M. Borwein, Moors, Warren B., Shawn Xianfu Wang
Publication date: 5 July 2001
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02820-3
differentiabilitysubdifferentialsBaire category\(T\)-Lipschitz functioncuscoupper semi-continuous set-valued map
Related Items (17)
Variational analysis of paraconvex multifunctions ⋮ Unnamed Item ⋮ Generalisations, examples, and counter-examples in analysis and optimisation. \textit{In honour of Michel Théra at 70} ⋮ Path differentiability of ODE flows ⋮ Three examples of residual pathologies ⋮ Conservative parametric optimality and the ridge method for tame min-max problems ⋮ Subgradient projectors: extensions, theory, and characterizations ⋮ Approximation and optimization of higher order discrete and differential inclusions ⋮ A derivative for complex Lipschitz maps with generalised Cauchy-Riemann equations ⋮ Upper semismooth functions and the subdifferential determination property ⋮ A differential operator and weak topology for Lipschitz maps ⋮ Unnamed Item ⋮ Some weighted sum formulas for multiple zeta, Hurwitz zeta, and alternating multiple zeta values ⋮ Every compact convex subset of matrices is the Clarke Jacobian of some Lipschitzian mapping ⋮ Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning ⋮ Lipschitz functions with maximal Clarke subdifferentials are staunch ⋮ Examples of Pathological Dynamics of the Subgradient Method for Lipschitz Path-Differentiable Functions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convex functions, monotone operators and differentiability.
- Differentiability of Lipschitz functions on Banach spaces
- Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings
- A continuity property related to Kuratowski's index of non-compactness, its relevance to the drop property, and its implications for differentiability theory
- Essentially smooth Lipschitz functions
- General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases
- Points of non-differentiability of typical Lipschitz functions
- Proximal analysis in smooth spaces
- A note on closed maps and compact sets
- Approximate subdifferentials and applications 3: the metric theory
- Optimization and nonsmooth analysis
- Approximate subdifferentials and applications II
- A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
- Subgradient representation of multifunctions
- Lipschitz functions with prescribed derivatives and subderivatives
- Variational Analysis
- Null Sets and Essentially Smooth Lipschitz Functions
- Geometric conditions of differentiability for a regular locally Lipschitz function
- Locally Lipschitz functions are generically pseudo-regular on separable Banach spaces
This page was built for publication: Generalized subdifferentials: a Baire categorical approach