 Stochastic Primal-Dual Hybrid Gradient (SPDHG) was proposed by Chambolle et al. (2018) and is a practical tool to solve nonsmooth large-scale optimization problems. In this paper we prove its almost sure convergence for convex but not necessarily strongly convex functionals. The proof makes use of a classical supermartingale result, and also rewrites the algorithm as a sequence of random continuous operators in the primal-dual space. We compare our analysis with a similar argument by Alacaoglu et al., and give sufficient conditions for an unproven claim in their proof .
The Stochastic Primal-Dual Hybrid Gradient (SPDHG) was proposed by Chambolle et al. (2018) and is an efficient algorithm to solve some nonsmooth large-scale optimization problems. In this paper we prove its almost sure convergence for convex but not necessarily strongly convex functionals. We also look into its application to parallel Magnetic Resonance Imaging reconstruction in order to test performance of SPDHG. Our numerical results show that for a range of settings SPDHG converges significantly faster than its deterministic counterpart .
A
The
R
a practical tool to solve
an efficient algorithm to solve some
R
The proof makes use of a classical supermartingale result, and also rewrites the algorithm as a sequence of random continuous operators in the primal-dual space. We compare our analysis with a similar argument by Alacaoglu et al., and give sufficient conditions for an unproven claim in their proof
We also look into its application to parallel Magnetic Resonance Imaging reconstruction in order to test performance of SPDHG. Our numerical results show that for a range of settings SPDHG converges significantly faster than its deterministic counterpart