Separable space

Algorithm

Extension (predicate logic)

Proximal Gradient Methods

Applied mathematics

Literature

Saddle

Computer science

Mathematical optimization

Filter (signal processing)

Mathematics

Sampling (signal processing)

Saddle point

Mathematical analysis

Geometry

Programming language

Dual (grammatical number)

Convex optimization

Regular polygon

Computer vision

SIAM Journal on Optimization

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth, strongly convex or fully smooth, strongly convex. We perform the analysis for arbitrary samplings of dual variables, and we obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications