Randomized Primal-Dual Proximal Block Coordinate Updates

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish its $O(1/t)$ convergence rate in terms of the objective value and feasibility measure. The framework includes several existing algorithms as special cases such … Read more

First-Order Algorithms for Convex Optimization with Nonseparate Objective and Coupled Constraints

In this paper we consider a block-structured convex optimization model, where in the objective the block-variables are nonseparable and they are further linearly coupled in the constraint. For the 2-block case, we propose a number of first-order algorithms to solve this model. First, the alternating direction method of multipliers (ADMM) is extended, assuming that it … Read more

On the Information-Adaptive Variants of the ADMM: an Iteration Complexity Perspective

Designing algorithms for an optimization model often amounts to maintaining a balance between the degree of information to request from the model on the one hand, and the computational speed to expect on the other hand. Naturally, the more information is available, the faster one can expect the algorithm to converge. The popular algorithm of … Read more