Related papers: Decomposition of flow data via gradient-based tran…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…
Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational…
We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…