Accelerated schemes with alternative step-size choices

Investigate accelerated primal–dual schemes using other relevant choices of step sizes.

Background

The paper develops regularization theory for non-accelerated Condat–Vũ and accelerated primal–dual hybrid gradient methods applied to linear inverse problems with additive noisy data. Its accelerated analysis uses a particular dynamically updated pair of primal and dual step sizes, chosen according to the strong convexity parameter and the acceleration strategy. The authors explicitly identify the investigation of accelerated schemes equipped with other relevant step-size choices as unresolved, suggesting a direction for extending the current convergence and error-estimate theory.