Related papers: Fairing of Discrete Planar Curves by Discrete Eule…

We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…

We address the problem of epipolar geometry using the motion of silhouettes. Such methods match epipolar lines or frontier points across views, which are then used as the set of putative correspondences. We introduce an approach that…

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…

As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…

There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning…

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…

We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an…

Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this…