2024/08/20 by Theo Diamandis, Guillermo Angeris, Diamandis, Theo +1
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Optimization and Control (math.OC) #Optimization and Search Problems #Scheduling and Optimization Algorithms
paper · pdf · doi:10.48550/arxiv.2408.11040
openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike the classic network flows literature, we also allow for a concave relationship between the input and output flows of edges. This nonlinear gain describes many physical phenomena, including losses in power network transmission lines. We outline an efficient algorithm for solving this problem which parallelizes over the graph edges. We provide an open source implementation of this algorithm in the Julia programming language package ConvexFlows.jl. This package includes an interface to easily specify these flow problems. We conclude by walking through an example of solving for an optimal power flow using ConvexFlows.