相关论文: Bringing regularized optimal transport to lightspe…

In this letter, we propose a new routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called {\it…

Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval. Fixed point analysis shows that the DRS iterated…

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…

This article reviews the use of first order convex optimization schemes to solve the discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier. We develop a staggered grid discretization that is well adapted…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…

In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…

We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…

We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in (Bredies and Fanzon, ESAIM: M2AN, 54:2351-2382, 2020), where the…

The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility…

DC Optimal Power Flow (DCOPF) is a key operational tool for power system operators, and it is embedded as a subproblem in many challenging optimization problems (e.g., line switching). However, traditional CPU-based solve routines (e.g.,…

Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…

We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the $L^p$ optimal transport with $L^p$ distance. For $p=1$, we derive the…

Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the…

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…