Related papers: Primal-dual method for searching equillibriums in …
In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…
As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality of the…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…
In this work, we construct a primal-dual forward-backward (PDFB) splitting method for computing a class of cross-diffusion systems that can be formulated as gradient flows under transport distances induced by matrix mobilities. By…
In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in…
We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization…
This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent,…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
Online optimisation facilitates the solution of dynamic inverse problems, such as image stabilisation, fluid flow monitoring, and dynamic medical imaging. In this paper, we improve upon previous work on predictive online primal-dual methods…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…