Related papers: Primal-dual method for searching equillibriums in …
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…
This paper investigates two accelerated primal-dual mirror dynamical approaches for smooth and nonsmooth convex optimization problems with affine and closed, convex set constraints. In the smooth case, an accelerated primal-dual mirror…
Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…
Lagrangian formulation of kinematic wave provides a more accurate representation than the most commonly used Eulerian formulation. Furthermore, Lagrangian representation offers a flexibility to study certain traffic phenomena (e.g. capacity…
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…
In vehicular traffic planning it is a long standing problem how to assign demand such on the available model of a road network that an equilibrium with regard to travel time or generalized costs is realized. For pedestrian traffic this…
The convergence of many proximal algorithms involving a gradient descent relies on its Lipschitz constant. To avoid computing it, backtracking rules can be used. While such a rule has already been designed for the forward-backward algorithm…
In this paper, we investigate traffic signal control in a network of interconnected intersections, aiming to balance lane-level vehicle densities through optimal green-time allocation. We develop a two-lane traffic flow model that…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
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…
We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics.…
In this paper we present a novel derivation for an existing node-based algorithm for distributed optimisation termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, in this work monotone operator theory…
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…
In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix $D$. Relaxing requirement on…
In this paper, based a novel primal-dual dynamical model with adaptive scaling parameters and Bregman divergences, we propose new accelerated primal-dual proximal gradient splitting methods for solving bilinear saddle-point problems with…
We propose a double obstacle phase field methodology for binary recovery of the slowness function of an Eikonal equation found in first traveltime tomography. We treat the inverse problem as an optimization problem with quadratic misfit…
This work studies distributed primal-dual strategies for adaptation and learning over networks from streaming data. Two first-order methods are considered based on the Arrow-Hurwicz (AH) and augmented Lagrangian (AL) techniques. Several…
In this book we describe BMW traffic assignment model and Nesterov-dePalma model. We consider Entropy model for demand matrix. Based on this models we build multi-stage traffic assignment models. The equilibrium in such models can be found…
Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…