Related papers: Global solutions of approximation problems in Krei…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M. Krein's spectral theory of J-selfadjoint operators is the Hilbert…
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…
This paper deals with approximate solutions of an optimization problem with interval-valued objective function. Four types of approximate solution concepts of the problem are proposed by considering the partial ordering $LU$ on the set of…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…
We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…
In this paper we survey a number of recent results concerning the existence and moduli spaces of solutions of various geometric problems on noncompact manifolds. The three problems which we discuss in detail are: I. Complete properly…
Consider a non-linear operator equation $x - K(x) = f$, where $f$ is a given function and $K$ is a Urysohn integral operator with Green's function type kernel defined on $L^\infty [0, 1]$. We apply approximation methods based on…
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast…
In its original formulation the Krein matrix was used to locate the spectrum of first-order star-even polynomial operators where both operator coefficients are nonsingular. Such operators naturally arise when considering first-order-in-time…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
We study various approximation results of solutions of equations $f(x,Y)=0$ where $f(x,Y)\in\mathbb K[[x]][Y]^r$ and $x$ and $Y$ are two sets of variables, and where some components of the solutions $y(x)\in\mathbb K[[x]]^m$ do not depend…
This paper studies the convergence properties of the inexact Jordan-Kinderlehrer-Otto (JKO) scheme and proximal-gradient algorithm in the context of Wasserstein spaces. The JKO scheme, a widely-used method for approximating solutions to…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to…
We consider the problem of finding the minimal number of points required to intersect all lines in an affine space over the finite field of order 3. We also consider the problem of finding the minimal number of points required to intersect…