An enhanced Baillon-Haddad theorem for convex functions on convex sets

2019/04/09 by Pedro Pérez-Aros, Pérez-Aros, Pedro, Emilio Vilches +1 · 1 citation
Computer Science · Mathematics · #47H05 #47H09 #47N10 #49J50 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1904.04885

openalex publication_date 2019/04/09 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28

Abstract

The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is β-Lipschitz if and only if it is 1/β-cocoercive. In this paper, we extend this theorem to Gâteaux differentiable convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of C^1,+ convex functions in terms of local cocoercitivity.

Citations

• The Baillon-Haddad Theorem Revisited
• Quelques propriétés des opérateurs angle-bornés etn-cycliquement monotones

Cited by

• Tikhonov-like regularization of dynamical systems associated with nonexpansive operators defined in closed and convex sets

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