Related papers: Efficient Fast Marching with Finsler metrics
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…
Wave propagation and scattering problems in acoustics are often solved with boundary element methods. They lead to a discretization matrix that is typically dense and large: its size and condition number grow with increasing frequency. Yet,…
Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics…
In robot localisation and mapping, outliers are unavoidable when loop-closure measurements are taken into account. A single false-positive loop-closure can have a very negative impact on SLAM problems causing an inferior trajectory to be…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…
We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares…
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better…
In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the…
We study the travel time tomography problem for transversely isotropic media using the artificial boundary method used in works in X-ray tomography and boundary rigidity problems. The analysis involved requires a modification of the…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
We describe a variation of the iterative closest point (ICP) algorithm for aligning two point sets under a set of transformations. Our algorithm is superior to previous algorithms because (1) in determining the optimal alignment, it…