A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions | Zendy

Hédy Attouch | Zendy; B. F. Svaiter | Zendy

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A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions

Author(s) -

Hédy Attouch,

B. F. Svaiter

Publication year - 2011

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/100784114

Subject(s) - monotone polygon , lipschitz continuity , differential inclusion , mathematics , hilbert space , discretization , dynamical systems theory , strongly monotone , lyapunov function , cauchy distribution , mathematical analysis , pure mathematics , nonlinear system , physics , geometry , quantum mechanics

International audienceWe introduce nonautonomous continuous dynamical systems which are linked to the Newton and Levenberg-Marquardt methods. They aim at solving inclusions governed by maximal monotone operators in Hilbert spaces. Relying on the Minty representation of maximal monotone operators as lipschitzian manifolds, we show that these dynamics can be formulated as first-order in time differential systems, which are relevant to the Cauchy-Lipschitz theorem. By using Lyapunov methods, we prove that their trajectories converge weakly to equilibria. Time discretization of these dynamics gives algorithms providing new insight into Newton's method for solving monotone inclusions

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