FIRST-ORDER METHODS FOR LARGE SCALE CONVEX AND NONCONVEX DISTRIBUTED COMPOSITE OPTIMIZATION PROBLEMS
Abstract
Since many problems in economics, natural sciences and engineering can be formulated as optimization problems, there is a high and increasing demand for more efficient algorithms and software packages for solving them. For example, large datasets are constantly being created due to the advent of the Internet where large amount of texts, images and videos are made available daily. Optimization is a critical tool for extracting useful information from these datasets. However, due to their huge size, there is a constant need to develop ever more efficient methods to solve the models that handle and extract information from them. Algorithmic advances to be studied in this project sit in the center of the pipeline of data to predictive models to decision analysis. Coupled with recent advances in statistical learning, as well as rapid rises in computing power and storage, the proposed research will help transform our ability to interpret increasingly large, noisy or incomplete datasets; to infer important new knowledge from the data; and to guide action and policies. The alternating direction method of multipliers (ADMM) is a simple but powerful algorithm for efficiently solving distributed optimization problems which appear in applications such as distributed matrix factorization, distributed clustering, asset allocation, and big data set handling. One of its main features is its potential to process huge datasets in a parallel and-or fully decentralized manner. While ADMM is quite well studied in the context of convex optimization, it is not so in the nonconvex setting. The objective of this project is to develop and study the complexity analyses of- 1) multiblock variants of the ADMM for solving linearly constrained nonconvex composite optimization problems without assuming a restrictive but popular last block condition; 2) first-order multi-agent distributed techniques for solving finite sum optimization problems and linearly constrained multiblock optimization problems; and 3) proximal bundle methods for solving convex and nonconvex nonsmooth composite optimization problems. This research will lead to new algorithms and software to efficiently solve a large class of optimization problems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502210088
Entities
People
- Renato Monteiro
Organizations
- Air Force Office of Scientific Research
- Georgia Tech Research Corporation
- United States Air Force