Related papers: On a general approach to some problems of approxim…

In this paper, approximation schemes are proposed for handling load uncertainty in compliance-based topology optimization problems, where the uncertainty is described in the form of a set of finitely many loading scenarios. Efficient…

This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

We solve the Stechkin problem about approximation of generally speaking unbounded hypersingular integral operators by bounded ones. As a part of the proof, we also solve several related and interesting on their own problems. In particular,…

We study the differential properties of generalized arc schemes, and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.

Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of…

The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

This paper offers a newly created integral approach for operators employing the orthogonal modified Laguerre polynomials and P\u{a}lt\u{a}nea basis. These operators approximate the functions over the interval $[0,\infty)$. Further, the…

As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…

This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…

A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues…

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate…

We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…