Inertial, corrected, primal-dual proximal splitting

Abstract

We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding correctors corresponding to the anti-symmetric part of the relevant monotone operator, using a FISTA-style gap unrolling argument, we are able to derive gap estimates instead of merely ergodic gap estimates. Moreover, based on adding a diagonal component to this corrector, we are able to combine strong convexity based acceleration with inertial acceleration. We test our proposed method on image processing and inverse problems problems, obtaining convergence improvements for sparse Fourier inversion and Positron Emission Tomography.

References in corpus (5)

• An inertial forward-backward algorithm for monotone inclusions
• Bilevel parameter learning for higher-order total variation regularisation models
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Cited by in corpus (1)

• First-order primal-dual methods for nonsmooth nonconvex optimisation