Related papers: Numerical integration without smoothness assumptio…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…
There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the…
It is natural to expect the following loosely stated approximation principle to hold: a numerical approximation solution should be in some sense as smooth as its target exact solution in order to have optimal convergence. For piecewise…
There is a large body of work on convergence rates either in passive or active learning. Here we outline some of the results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness and…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
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…
Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincide with a discretisation point, and the jumps in the function…
The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…
We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and…
Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…
A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…
Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this…