14 citations · 34 across the 20 of their papers we have counts for
23 papers
Difference of Convex (DC) approach for neural network approximation with uniform loss function
Vinesha Peiris, Nadezda Sukhorukova
Neural networks (NNs) can be viewed as approximation tools. Traditionally, NNs are relying on gradient and stochastic gradient (SG) methods. There are a number of available computa…
KAN vs LSTM Performance in Time Series Forecasting
Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova +1
This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of s…
KKT-based optimality conditions for neural network approximation
Vinesha Peiris, Nadezda Sukhorukova, Julien Ugon
In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in Manhattan ( norm) and Chebyshev ( norm). The op…
Nonsmooth Optimisation and neural networks
Vinesha Peiris, Nadezda Sukhorukova
In this paper, we study neural networks from the point of view of nonsmooth optimisation, namely, quasidifferential calculus. We restrict ourselves to the case of uniform approxima…
Bivariate rational approximations of the general temperature integral
Alireza Aghili, Nadezda Sukhorukova, Julien Ugon
The non-isothermal analysis of materials with the application of the Arrhenius equation involves temperature integration. If the frequency factor in the Arrhenius equation depends…
Best free knot linear spline approximation and its application to neural networks
Vinesha Peiris, Duy Khoa Pham, Nadezda Sukhorukova
The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable,…
A comparison of rational and neural network based approximations
Vinesha Peiris, Reinier Diaz Millan, Nadezda Sukhorukova +1
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lips…
Variational properties of the abstract subdifferential operator
Reinier Diàz Millàn, Nadezda Sukhorukova, Julien Ugon
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear…
Application and issues in abstract convexity
Reinier Díaz Millán, Nadezda Sukhorukova, Julien Ugon
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly conc…
Deep Learning with Nonsmooth Objectives
Vinesha Peiris, Nadezda Sukhorukova, Vera Roshchina
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network. We hypothesise that this may lead to superior cl…
Multivariate approximation by polynomial and generalised rational functions
R. Díaz Millán, V. Peiris, N. Sukhorukova +1
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and…
The extension of linear inequality method for generalised rational Chebyshev approximation to approximation by general quasilinear functions
Vinesha Peiris, Nadezda Sukhorukova
In this paper we demonstrate that a well known linear inequality method developed for rational Chebyshev approximation is equivalent to the application of the bisection method used…
An algorithm for best generalised rational approximation of continuous functions
R. Díaz Millán, Nadezda Sukhorukova, Julien Ugon
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation p…
Uniqueness of solutions in multivariate Chebyshev approximation problems
Vera Roshchina, Nadia Sukhorukova, Julien Ugon
We study the solution set to multivariate Chebyshev approximation problem, focussing on the ill-posed case when the uniqueness of solutions can not be established via strict polyno…
Solving multi-resource allocation and location problems in disaster management through linear programming
Behrooz Bodaghi, Nadezda Sukhorukova
In this paper we propose a new efficient linear programming based approach for multi-resource allocation and location problems in disaster management. Such problems require an inte…
Two curve Chebyshev approximation and its application to signal clustering
Nadezda Sukhorukova
In this paper we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need f…
Schur functions for approximation problems
Nadezda Sukhorukova, Julien Ugon
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinato…
Alternance Theorems and Chebyshev Splines Approximation
Jean-Pierre Crouzeix, Nadezda Sukhorukova, Julien Ugon
One of the purposes in this paper is to provide a better understanding of the alternance property which occurs in Chebyshev polynomial approximation and piecewise polynomial approx…
Chebyshev multivariate polynomial approximation and point reduction procedure
Nadezda Sukhorukova, Julien Ugon, David Yost
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on th…
A generalisation of de la Vallée-Poussin procedure to multivariate approximations
Nadezda Sukhorukova, Julien Ugon
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is,…
Chebyshev approximation for multivariate functions
Nadezda Sukhorukova, Julien Ugon, David Yost
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is ver…
Linear least squares problems involving fixed knots polynomial splines and their singularity study
Zahra Roshan Zamir, Nadezda Sukhorukova
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial s…
Characterization theorem for best polynomial spline approximation with free knots
Nadezda Sukhorukova, Julien Ugon
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions. We apply nonsmooth nonconvex analysis to obtain this result, which is als…