Collaborative Proposal: Optimal Methods for Nonlinearly Coupled Distributed Optimization
Abstract
The primary objective of this research is to develop fundamental theory and algorithms for solving distributed optimization and variational inequality problems with nonlinearly coupled objective or constraints. Distributed optimization refers to a class of optimization problems where distributed agents work together to achieve a certain objective. Distributed optimization differs significantly from traditional centralized optimization in that one needs to consider the tradeoff between the communication cost and computation cost under different network topologies. It plays a critically important role in the design, operations and utilization of advanced communication networks. In spite of many recent research efforts that have been devoted to distributed optimization, existing methods are inadequate in dealing with more and more complex distributed optimization problems arising from the consideration of robustness, risk aversion, competition, and fairness. In particular, existing distributed optimization focuses on minimizing the summation (or average) of the cost functions of all agents, and cannot handle the nonlinearly coupled objective and/or constraints mentioned above.This research focuses on the following three fundamental problems in the area of distributed optimization:i) How to design efficient distributed methods for risk-averse objectives in terms of their communication, computation, and sampling complexities;ii) Howto handle coupling function constraints under the distributed setting in a verifiable manner;and iii) How to design efficient methods for distributed equilibrium or variational inequalities possibly with shared function constraints when competition exists among agents.If successful, this research will result in a new set of efficient optimization methods, including distributed risk-averse optimization and constrained operator extrapolation methods, for solving constrained and nonlinearly coupled distributed optimization problems. It is expected that these methods can judiciously skip expensive operations, such as communication rounds, but still maintain the best possible performance guarantees in terms of computation or sampling. This research will further explore the applicationsof these algorithms for a variety of enabling technologies for drone communication that are directly relevant to the Navy s operations and mission.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2024
- Source ID
- N000142412749
Entities
People
- Digvijay Boob
Organizations
- Office of Naval Research
- Southern Methodist University
- United States Navy