Related papers: Linear Programming and Kantorovich Spaces
We consider linear narrow operators on lattice-normed spaces. We prove that, under mild assumptions, every finite rank linear operator is strictly narrow (before it was known that such operators are narrow). Then we show that every…
We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\le A \le M$. Then for every unital positive linear map $\Phi$, \[\Phi(A^{-1})^2\le (\frac{(M+m)^2}{4Mm})^2\Phi(A)^{-2}.\]…
In this paper, we present some applications of the multivariate sampling Kantorovich operators $S_w$ to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show…
Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…
This brief text is in memory of Professor Ivan Kupka. It presents his vision, scientific life, his interest in mathematics and our join collaboration.
The goal of this thesis is to study the use of the Kantorovich-Rubinstein distance as to build a descriptor of sample complexity in classification problems. The idea is to use the fact that the Kantorovich-Rubinstein distance is a metric in…
We discuss the method recently proposed by S. Chubanov for the linear feasibility problem. We present new, concise proofs and interpretations of some of his results. We then show how our proofs can be used to find strongly polynomial time…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…
The prominent Russian mathematician Igor Rostislavovich Shafarevich passed away on February 19, 2017. In this article we supply his biography, discuss his many important contributions to number theory, algebra and algebraic geometry, and…
The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
This article concerns the life and work of Lucjan Emil B\"ottcher (1872-1937), a Polish mathematician. Besides biographical and bibliographical information, it contains a survey of his mathematical achievements in the theory of iteration…
We study two topologies $\tau_{KR}$ and $\tau_K$ on the space of measures on a completely regular space generated by Kantorovich--Rubinshtein and Kantorovich seminorms analogous to their classical norms in the case of a metric space. The…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between…
In this paper, we study the order of approximation for max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. We establish a quantitative estimate for the considered family of…