Collaborative Proposal: Optimal Methods for Nonlinearly Coupled Distributed Optimization
Abstract
The primary objective of this research is to develop fundamental theory and algorithms forsolving distributed optimization and variational inequality problems with a nonlinearly coupledobjective or constraints. Distributed optimization refers to a class of optimization problems wheredistributed agents work together to achieve a certain objective. Distributed optimization differssignificantly from traditional centralized optimization in that one needs to consider the tradeoffbetween the communication cost and computation cost under different network topologies. It playsa critically important role in the design, operations and utilization of advanced communicationnetworks. In spite of many recent research efforts that have been devoted to this area, existingmethods are inadequate indealing with more and more complex distributed optimization problemsarising from the consideration of robustness, risk aversion, competition, and fairness. In particular,existing distributed optimization focuses on minimizing the summation (or average) of the costfunctions of all agents, and cannot handle the nonlinearly coupled objective and/or constraintsmentioned above.This research focuses on the following three fundamental problems in the area of distributedoptimization: i) How to design efficient distributed methodsfor risk-averse objectives in terms oftheir communication, computation, and sampling complexities; ii) How to handle coupling functionconstraints under the distributed setting in a verifiable manner; and iii) How to design efficientmethods for distributed equilibrium or variational inequalities possibly with shared function constraintswhen competition exists among agents. If successful, this research will result in a new setof efficient optimization methods, including distributed risk-averse optimization and constrainedoperator extrapolation methods, for solving constrained and nonlinearly coupled distributed optimizationproblems. It is expected that these methods can judiciously skip expensive operations,such as communication rounds, but still maintain the best possible performance guarantees in termsof computation or sampling. This research will further explore the applications of these algorithmsfor a variety of enabling technologies for drone communication that are directly relevant to theNavy#s operations and mission.THIS ABSTRACT IS APPROVED FOR PUBLIC RELEASE
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2024
- Source ID
- N000142412654
Entities
People
- Guanghui Lan
Organizations
- Georgia Tech Research Corporation
- Office of Naval Research
- United States Navy