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math.OC2024
The Convex Geometry of Network Flows
Theo Diamandis, Guillermo Angeris
In this paper, we derive a number of interesting properties and extensions of the convex flow problem from the perspective of convex geometry. We show that the sets of allowable fl…
math.OC2024
Solving the Convex Flow Problem
Theo Diamandis, Guillermo Angeris
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 fu…
math.OC2024
Convex Network Flows
Theo Diamandis, Guillermo Angeris, Alan Edelman
We introduce a general framework for flow problems over hypergraphs. In our problem formulation, which we call the convex flow problem, we have a concave utility function for the n…