相关论文: An optimal irrigation network with infinitely many…
The optimization version of the cavity method for single instances, called Max-Sum, has been applied in the past to the Minimum Steiner Tree Problem on Graphs and variants. Max-Sum has been shown experimentally to give asymptotically…
We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen…
In this paper we introduce an optimal control approach to Richards' equation in an irrigation framework, aimed at minimizing water consumption while maximizing root water uptake. We first describe the physics of the nonlinear model under…
We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation…
We present a specialized network simplex algorithm for the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total…
The paper addresses design/building frameworks for some kinds of tree-like and hierarchical structures of systems. The following approaches are examined: (1) expert-based procedures, (2) hierarchical clustering; (3) spanning problems (e.g.,…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Increasing concerns on the security and quality of water distribution systems (WDS), call for computational tools with performance guarantees. To this end, this work revisits the physical laws governing water flow and provides a hierarchy…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network…
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the…
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
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 flows always can be imbued with a downward closure property,…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…