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P6: The Alternating Direction Method of Multipliers. An Adaptive Step-size Software Library
Author: Peter Sutor , Advisor: Tom Goldstein (CS)
Problem Statement Presentation
Project Proposal
Abstract
The Alternating Direction Method of Multipliers (ADMM) is a method that solves convex optimization problems of the form min(f(x) + g(z)) subject to Ax + Bz = c, where A and B are suitable matrices and c is a vector, for optimal points (xopt; zopt). It is commonly used for distributed convex minimization on large scale data-sets. However, it can be technically difficult to implement and there is no known way to automatically choose an optimal step size for ADMM. Our goal in this project is to simplify the use of ADMM by making a robust, easy-to-use software library for all ADMM-related needs, with an adaptive step-size selection algorithm to optimize performance on every iteration. The library will contain a general ADMM method, as well as solvers for common problems that ADMM is used for. It will also implement adaptive step-size selection, utilize the Message Passing Interface (MPI) for parallel computing and have user-friendly options and features.
MidYear Progress Report and
Presentation
Final Presentation ,
Final Report
