40 research outputs found
Four Operator Splitting via a Forward-Backward-Half-Forward Algorithm with Line Search
In this article we provide a splitting method for solving monotone inclusions
in a real Hilbert space involving four operators: a maximally monotone, a
monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The
proposed method takes advantage of the intrinsic properties of each operator,
generalizing the forward-back-half forward splitting and the Tseng's algorithm
with line-search. At each iteration, our algorithm defines the step-size by
using a line search in which the monotone-Lipschitzian and the cocoercive
operators need only one activation. We also derive a method for solving
non-linearly constrained composite convex optimization problems in real Hilbert
spaces. Finally, we implement our algorithm in a non-linearly constrained
least-square problem, and we compare its performance with available methods in
the literature.Comment: 17 page
A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions
We introduce a framework based on Rockafellar's perturbation theory to
analyze and solve general nonsmooth convex minimization and monotone inclusion
problems involving nonlinearly composed functions as well as linear
compositions. Such problems have been investigated only from a primal
perspective and only for nonlinear compositions of smooth functions in
finite-dimensional spaces in the absence of linear compositions. In the context
of Banach spaces, the proposed perturbation analysis leads to the construction
of a dual problem and of a maximally monotone Kuhn--Tucker operator which is
decomposable as the sum of simpler monotone operators. In the Hilbertian
setting, this decomposition leads to block-iterative primal-dual proximal
algorithms that fully split all the components of the problem and capture
state-of-the-art existing methods as special cases