Related papers: Fast Mesh Refinement in Pseudospectral Optimal Con…
We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
Most adaptive optics (AO) systems using pyramid wavefront sensors (PyWFS) to estimate the phase of the pupil field use mechanical modulation of the beam in order to increase the dynamic range in low-order modes so the PyWFS can usefully…
Finetuning a pretrained model has become a standard approach for training neural networks on novel tasks, resulting in fast convergence and improved performance. In this work, we study an alternative finetuning method, where instead of…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…
Particle Swarm Optimization technique offers optimal or suboptimal solution to multidimensional rough objective functions. In this paper, this optimization technique is used for designing fractional order PID controllers that give better…
We study convex-concave saddle point problems with bilinear coupling, covering linearly constrained convex optimization and more general nonsmooth or constrained models via a proximable term in the dual objective. In linearly convergent…
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…
Improved EM strategies, based on the idea of efficient data augmentation (Meng and van Dyk 1997, 1998), are presented for ML estimation of mixture proportions. The resulting algorithms inherit the simplicity, ease of implementation, and…
The amplitude of resonant oscillations in a non-Hermitian environment can either decay or grow in time, corresponding to a mode with either loss or gain. When two coupled modes have a specific difference between their loss or gain, a…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…