Related papers: The Budgeted Transportation Problem
$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…
We study the load balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
A new method is proposed for the solution of the data-driven optimal transport barycenter problem and of the more general distributional barycenter problem that the article introduces. The method improves on previous approaches based on…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and…
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…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The…
This paper studies a portfolio allocation problem, where the goal is to prescribe the wealth distribution at the final time. We study this problem with the tools of optimal mass transport. We provide a dual formulation which we solve by a…
In the Stackelberg Network Pricing problem, one has to assign tariffs to a certain subset of the arcs of a given transportation network. The aim is to maximize the amount paid by the user of the network, knowing that the user will take a…
To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered…
We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example,…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…