A cut-and-project perspective for linearized Bregman iterations
arxiv(2024)
摘要
The linearized Bregman iterations (LBreI) and its variants are powerful tools
for finding sparse or low-rank solutions to underdetermined linear systems. In
this study, we propose a cut-and-project perspective for the linearized Bregman
method via a bilevel optimization formulation, along with a new unified
algorithmic framework. The new perspective not only encompasses various
existing linearized Bregman iteration variants as specific instances, but also
allows us to extend the linearized Bregman method to solve more general inverse
problems. We provide a completed convergence result of the proposed algorithmic
framework, including convergence guarantees to feasible points and optimal
solutions, and the sublinear convergence rate. Moreover, we introduce the
Bregman distance growth condition to ensure linear convergence. At last, our
findings are illustrated via numerical tests.
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