Related papers: Application and issues in abstract convexity
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…
Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…
We investigate the associativity property for functions of indefinite arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.
We address a deep study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals as well as those raised by the power-law approximation of such functionals. Our quest is motivated by the…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…
In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some…