The kernel average for two convex functions and its application to the extension and representation of monotone operators

By Heinz H. Bauschke, Xianfu Wang. 2009

61 citations recorded by the source corpus.

We provide and analyze an average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also known as selfdual Lagrangian) which can be used for finding an explicit maximal monotone extension of the given monotone operator. This completely settles one of the open problems posed by Fitzpatrick in the setting of reflexive Banach spaces.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c50033d07805555cc50f3461cb9ce8912fc3f1e5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Lipschitz Regularity for Elliptic Equations with Random Coefficients (2014, methodology): “In the second step, we use F̃ to construct a representative F of a that is also self-dual, following an approach due to [6].”