Multivariate Monotone Inclusions in Saddle Form

Autor: Patrick L. Combettes, Minh Bui

Publikováno v: Mathematics of Operations Research. 47:1082-1109

We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and Lipschitzian monoto

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::59192898b47cfde22675bdae380c15b3
https://doi.org/10.1287/moor.2021.1161

Solving Composite Fixed Point Problems with Block Updates

Autor: Lilian E. Glaudin, Patrick L. Combettes

Publikováno v: Advances in Nonlinear Analysis, Vol 10, Iss 1, Pp 1154-1177 (2021)

Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d2a5a69c373bb00b9a09c7202bfb4d9
https://doaj.org/article/0000d55fc13d415094eebd51277b0630

Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators

Autor: Patrick L. Combettes, Jean-Christophe Pesquet

Publikováno v: SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science, 2020, ⟨10.1137/19M1272780⟩
SIAM Journal on Mathematics of Data Science, Society for Industrial and Applied Mathematics, 2020, ⟨10.1137/19M1272780⟩

International audience; Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robust-ness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6822e1c81b90a70c344e7825e9e16520
https://doi.org/10.1137/19m1272780

Reconstruction of Functions from Prescribed Proximal Points

Autor: Zev C. Woodstock, Patrick L. Combettes

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be represented using

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54e56f6a5eaa27c5554fabb50ed33f6f

Deep Neural Network Structures Solving Variational Inequalities *

Autor: Jean-Christophe Pesquet, Patrick L. Combettes

Publikováno v: Set-Valued and Variational Analysis
Set-Valued and Variational Analysis, Springer, In press, ⟨10.1007/s11228-019-00526-z⟩
Set-Valued and Variational Analysis, In press, ⟨10.1007/s11228-019-00526-z⟩

International audience; Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation opera

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6581a1df515cdb8ba7794e9d5bb894e9
https://hal.archives-ouvertes.fr/hal-02425025/document