Abstract
AbstractIn the previous paper Bello-Cruz et al. (J Optim Theory Appl 188:378–401, 2021), we showed that the quadratic growth condition plays a key role in obtaining Q-linear convergence of the widely used forward–backward splitting method with Beck–Teboulle’s line search. In this paper, we analyze the property of quadratic growth condition via second-order variational analysis for various structured optimization problems that arise in machine learning and signal processing. This includes, for example, the Poisson linear inverse problem as well as the $$\ell _1$$
ℓ
1
-regularized optimization problems. As a by-product of this approach, we also obtain several full characterizations for the uniqueness of optimal solution to Lasso problem, which complements and extends recent important results in this direction.
Funder
Australian Research Council
National Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Management Science and Operations Research,Control and Optimization
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