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An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

Optimization and Control · Mathematics 2016-03-09 Alexander Gasnikov , Evgenia Gasnikova , Sergey Matsievsky , Inna Usik

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Chuan-Xi Zhu , Meng Wen , Ji-Gen Peng

This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…

Computer Vision and Pattern Recognition · Computer Science 2015-03-17 Julien Rabin , Nicolas Papadakis

This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…

Probability · Mathematics 2017-10-31 Teemu Pennanen , Ari-Pekka Perkkiö

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

Optimization and Control · Mathematics 2021-04-13 Renbo Zhao

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

Optimization and Control · Mathematics 2015-07-06 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting…

Optimization and Control · Mathematics 2024-10-15 Dongjun Wu , Anders Rantzer

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

Optimization and Control · Mathematics 2020-06-23 Pascal Bianchi , Walid Hachem , Adil Salim

We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…

Machine Learning · Computer Science 2023-03-02 Alexander Korotin , Daniil Selikhanovych , Evgeny Burnaev

We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing…

Analysis of PDEs · Mathematics 2019-07-22 Guy Bouchitté , Giuseppe Buttazzo , Thierry Champion , Luigi De Pascale

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the…

Optimization and Control · Mathematics 2020-07-13 A. K. Das , Deepmala , R. Jana

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…

Numerical Analysis · Mathematics 2016-02-09 Alper Korkmaz

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

Numerical Analysis · Mathematics 2020-04-01 Carolin Dirks , Benedikt Wirth

We study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…

Optimization and Control · Mathematics 2023-01-02 Toshio Mikami , Haruka Yamamoto

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…

Optimization and Control · Mathematics 2024-06-21 Kevin Tracy , Zachary Manchester

Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…

Optimization and Control · Mathematics 2012-11-21 Yan-Qin Bai , Chuan-Hao Guo

In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…

Systems and Control · Computer Science 2018-06-15 Ivano Notarnicola , Giuseppe Notarstefano

We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…

Optimization and Control · Mathematics 2024-12-03 Jean-David Benamou , Guillaume Chazareix , Grégoire Loeper

We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…

Analysis of PDEs · Mathematics 2015-05-08 Luigi De Pascale