Characterization of Lower Semicontinuous Convex Functions
- 1 September 1992
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 116 (1), 67-72
- https://doi.org/10.2307/2159295
Abstract
We prove that a lower semicontinuous function defined on a reflexive Banach space is convex if and only if its Clarke subdifferential is monotone.Keywords
This publication has 9 references indexed in Scilit:
- Subgradient monotonicity and convex functionsNonlinear Analysis, 1990
- Optimization and Nonsmooth AnalysisPublished by Society for Industrial & Applied Mathematics (SIAM) ,1990
- Approximate mean value theorem for upper subderivativesNonlinear Analysis, 1988
- The Proximal Normal Formula in Banach SpaceTransactions of the American Mathematical Society, 1987
- Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: ApplicationsCanadian Journal of Mathematics, 1987
- An application of Ekeland's theorem to minimax problemsNonlinear Analysis, 1982
- Generalized Directional Derivatives and Subgradients of Nonconvex FunctionsCanadian Journal of Mathematics, 1980
- Geometry of Banach Spaces-Selected TopicsLecture Notes in Mathematics, 1975
- Convex AnalysisPublished by Walter de Gruyter GmbH ,1970