Related papers: Dynamic interpolation for obstacle avoidance on Ri…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
Deep reinforcement learning algorithms typically act on the same set of actions. However, this is not sufficient for a wide range of real-world applications where different subsets are available at each step. In this thesis, we consider the…
In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
The subgradient method for convex optimization problems on complete Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. Iteration-complexity bounds of the subgradient method with exogenous step-size and…
In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in…
Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization…
Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
Variational interpolants are an indispensable tool for the construction of gradient-flow solutions via the Minimizing Movement Scheme. The De Giorgi lemma provides the associated discrete energy-dissipation inequality. It was originally…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig…
The solution of an extended Riemann problem is used to provide the internal boundary conditions at a junction when simulating one-dimensional flow through an open channel network. The proposed approach, compared to classic junction models,…
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…
The problem of the low-energy highly-anharmonic quantum dynamics of isolated impurities in solids is addressed by using path-integral Monte Carlo simulations. Interstitial oxygen in silicon is studied as a prototypical example showing such…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…