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Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport…
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
This study proposes a new constraint handling technique for assisting metaheuristic optimization algorithms to solve constrained optimization problems more effectively and efficiently. Given any two solutions of any constrained optimization…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
In the last fifteen years a significant progress was achieved by considering an entropic relaxation of the classical multi-partite optimal transport problem (MPOTP). The entropic relaxation gives rise to the rescaling problem of a given…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Trajectory optimization is the core of modern model-based robotic control and motion planning. Existing trajectory optimizers, based on sequential quadratic programming (SQP) or differential dynamic programming (DDP), are often limited by…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
In this paper, we study a spline collocation method for a numerical solution to the optimal transport problem We mainly solve the \MAE with the second boundary condition numerically by proposing a center matching algorithm. We prove a…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
This paper describes the implementation of a new interior point solver for linear programming for the open-source optimization library HiGHS. The solver uses a direct factorisation to solve the Newton systems, choosing the best approach…
The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…