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Sub differential Monotonicity as Characterization of Convex Functions |
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| Authors: | Rafael Correa Alejandro Jofrè Lionel Thibault |
| Affiliation: | 1. Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática , Universidad de Chile, Casilla 170-3 correo 3, Santiago, Chile;2. Departement de Mathèmatiques , Université de Pau , Av. de i'Universitè, Pau, 64000, France |
| Abstract: | We prove that a lower semicontinuous function defined on a Banach space is convex if and only if its subdifferential ismonotone. |
| Keywords: | Ill-posed problems Inverse problems Lavrentiev regularization A priori parameter choice Discrepancy principle Hilbert scales Monotone operators AMS Subject Classifications: 65J20 65M30 |