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Mastering dexterous robotic manipulation of deformable objects is vital for overcoming the limitations of parallel grippers in real-world applications. Current trajectory optimisation approaches often struggle to solve such tasks due to the…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified…
Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling…
Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…
This study applies the RBF wavelet series to the evaluation of analytical solutions of linear time-dependent wave and diffusion problems of any dimensionality and geometry. To the best of the author's knowledge, such analytical solutions…
Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the…
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based…
Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
In this paper, we propose a robust and efficient quadrotor motion planning system for fast flight in 3-D complex environments. We adopt a kinodynamic path searching method to find a safe, kinodynamic feasible and minimum-time initial…
The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal…
The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…
This paper presents a numerical algorithm for computing 6-degree-of-freedom free-final-time powered descent guidance trajectories. The trajectory generation problem is formulated using a unit dual quaternion representation of the rigid body…
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…
Training recurrent neural networks (RNNs) remains a challenge due to the instability of gradients across long time horizons, which can lead to exploding and vanishing gradients. Recent research has linked these problems to the values of…
A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform…
We examine directed spanners through flow-based linear programming relaxations. We design an $\~O(n^{2/3})$-approximation algorithm for the directed $k$-spanner problem that works for all $k\geq 1$, which is the first sublinear…