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We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an…
Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We study the optimization of navigational graph queries, i.e., queries which combine recursive and pattern-matching fragments. Current approaches to their evaluation are not effective in practice. Towards addressing this, we present a…
We propose in this article an adaptation of the basic techniques of the deterministic network calculus theory to the road traffic flow theory. Network calculus is a theory based on min-plus algebra. It uses algebraic techniques to compute…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
Many real life queueing networks have finite buffers with overflows. To understand the behavior of such networks, we consider traffic equations that generalize the traffic equations of classic open queueing networks where some nodes are…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems,…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We combine the power flow model with the proportionally fair optimization criterion to study the control of congestion within a distribution electric grid network. The form of the mathematical optimization problem is a convex second order…
Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model to simulate the motion of…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…