Related papers: Globally Solving Unbalanced Optimal Transport and …
We consider control systems governed by nonlinear O.D.E.'s that are affine in the time-derivative du/dt of the control u. The latter is allowed to be an integrable, possibly of unbounded variation function, which gives the system an…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…
We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…
We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast and anycast traffic, in a general wireless network. We propose an online dynamic policy, called…
The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts'…
Clustering is a fundamental task in the computer vision and machine learning community. Although various methods have been proposed, the performance of existing approaches drops dramatically when handling incomplete high-dimensional data…
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a constructive method, alternating minimizing movements for the…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
We consider the finite horizon optimal steering of the joint state probability distribution subject to the angular velocity dynamics governed by the Euler equation. The problem and its solution amounts to controlling the spin of a rigid…
We analyze controlled mass transportation plans with free end-time that minimize the transport cost induced by the generating function of a Lagrangian within a bounded domain, in addition to costs incurred as export and import tariffs at…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
Evaluating lesion evolution in longitudinal CT scans of can cer patients is essential for assessing treatment response, yet establishing reliable lesion correspondence across time remains challenging. Standard bipartite matchers, which rely…