Randomized Methods

A Flexible Coordinate Descent Method

We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust …

Avoiding Synchronization in First-Order Methods for Sparse Convex Optimization

Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML). However, the scalability of these optimization methods is inhibited by the cost of communicating …

Avoiding communication in primal and dual block coordinate descent methods

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large machine …

A Randomized Rounding Algorithm for Sparse PCA

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. In the proposed approach, we first solve an l1-penalized version of the NP-hard sparse PCA optimization problem and then we use a …