Solving monotone inclusions with linear multi-step methods
نویسندگان
چکیده
منابع مشابه
Solving monotone inclusions with linear multi-step methods
In this paper a new class of proximal-like algorithms for solving monotone inclusions of the form T (x) 3 0 is derived. It is obtained by applying linear multi-step methods (LMM) of numerical integration in order to solve the differential inclusion ẋ(t) ∈ −T (x(t)), which can be viewed as a generalization of the steepest decent method for a convex function. It is proved that under suitable cond...
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This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the H...
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We introduce non-autonomous 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, whi...
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In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative sc...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2003
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-002-0366-2