Newton-Like Dynamics and Forward-Backward Methods for Structured Monotone Inclusions in Hilbert Spaces |
| |
Authors: | B Abbas H Attouch Benar F Svaiter |
| |
Institution: | 1. I3M UMR CNRS 5149, Université Montpellier II, Place Eugène Bataillon, 34095, Montpellier, France 2. IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
|
| |
Abstract: | In a Hilbert space setting we introduce dynamical systems, which are linked to Newton and Levenberg–Marquardt methods. They are intended to solve, by splitting methods, inclusions governed by structured monotone operators M=A+B, where A is a general maximal monotone operator, and B is monotone and locally Lipschitz continuous. Based on the Minty representation of A as a Lipschitz manifold, we show that these dynamics can be formulated as differential systems, which are relevant to the Cauchy–Lipschitz theorem, and involve separately B and the resolvents of A. In the convex subdifferential case, by using Lyapunov asymptotic analysis, we prove a descent minimizing property and weak convergence to equilibria of the trajectories. Time discretization of these dynamics gives algorithms combining Newton’s method and forward-backward methods for solving structured monotone inclusions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|