Related papers: Adaptive strategies for solving parameterized syst…
In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some…
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…
In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…
Generally, multi-objective optimisation problems are solved exactly or approximated by solving a series of scalarisations, for example by dichotomic search. In this paper, we take a different approach and attempt to compute the set of all…
Machine learning has achieved remarkable success over the past couple of decades, often attributed to a combination of algorithmic innovations and the availability of high-quality data available at scale. However, a third critical component…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem --…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
In this work, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…