Flexible Parallel Algorithms for Big Data Optimization
The authors propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable non-smooth, convex one. The latter term is typically used to enforce structure in the solution as, for example, in Lasso problems. Their framework is very flexible and includes both fully parallel Jacobi schemes and Gauss-Seidel (Southwell-type) ones, as well as virtually all possibilities in between (e.g., gradient- or Newton-type methods) with only a subset of variables updated at each iteration. Their theoretical convergence results improve on existing ones, and numerical results show that the new method compares favorably to existing algorithms.