Convex Network Flows - Optimization Framework and Applications
Explore a comprehensive framework for modeling flow problems over hyper graphs in this 25-minute talk from The Julia Programming Language. Dive into a generalized approach that allows networks to have concave utility functions dependent on net flow at each node and edge. Learn how this framework encompasses traditional network optimization problems and their extensions, including max-flow and min-cost-flow with concave edge gain functions. Discover practical applications in optimal power flow with lossy transmission lines and resource allocation in wireless networks. Examine the dual problem that decomposes over edges, resulting in a fast, parallelizable algorithm. Gain insights into the implementation of this algorithm in the Julia package ConvexFlows.jl, which outperforms commercial solvers. Understand how modeling tools from the JuMP ecosystem facilitate easy problem specification within this framework, eliminating the need for direct conic form input.