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The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility…

Optimization and Control · Mathematics 2020-04-14 Heinz H. Bauschke , Minh N. Dao , Dominikus Noll , Hung M. Phan

We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by $$ -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular datum,…

Analysis of PDEs · Mathematics 2019-07-23 Francescantonio Oliva , Francesco Petitta

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…

Optimization and Control · Mathematics 2026-05-14 Frank E. Curtis , Lingjun Guo , Daniel P. Robinson

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

Optimization and Control · Mathematics 2023-05-04 Daniel Dörfler

We introduce and discuss the method of Linear Delta Expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules. Calculations are carried out up to two-loops and an…

High Energy Physics - Theory · Physics 2008-11-26 M. C. B. Abdalla , J. A. Helayël-Neto , Daniel L. Nedel , Carlos R. Senise

Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine…

High Energy Physics - Theory · Physics 2009-10-31 A. I. Davydychev , M. Yu. Kalmykov

Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…

Programming Languages · Computer Science 2025-08-22 Jingbo Wang , Shashin Halalingaiah , Weiyi Chen , Chao Wang , Isil Dillig

A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…

Combinatorics · Mathematics 2018-12-17 Julien Baste , Maximilian Fürst , Dieter Rautenbach

Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…

Classical Analysis and ODEs · Mathematics 2017-08-24 Fred Brackx , Frank Sommen , Jasson Vindas

The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…

Statistical Mechanics · Physics 2009-11-07 Asa Ben-Hur , Joshua Feinberg , Shmuel Fishman , Hava T. Siegelmann

The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…

Optimization and Control · Mathematics 2018-03-28 Ivan V. Kazachkov

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…

Data Structures and Algorithms · Computer Science 2016-03-01 László A. Végh

We propose and study a generalization to the well-known problem of polyline simplification. Instead of a single polyline, we are given a set of $\ell$ polylines possibly sharing some line segments and bend points. Our goal is to minimize…

Computational Geometry · Computer Science 2020-06-24 Joachim Spoerhase , Sabine Storandt , Johannes Zink

We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function $f = [x_0, x_1, x_2, x_3]$, we prove that the bipartite Holant…

Computational Complexity · Computer Science 2020-11-19 Austen Z. Fan , Jin-Yi Cai

We introduce and study new versions of polylogarithms and a zeta function on a completion of $\mathbb F_q (x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for $\mathbb F_q$-linear functions.

Number Theory · Mathematics 2007-05-23 Anatoly N. Kochubei

We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…

Data Structures and Algorithms · Computer Science 2011-01-21 Abhimanyu Das , David Kempe

In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…

Statistics Theory · Mathematics 2007-11-29 J. Cupidon , D. S. Gilliam , R. Eubank , F. Ruymgaart

Propositional dynamic logic (PDL) is an important modal logic used to specify and reason about the behavior of software. A challenging problem in the context of PDL is solving fixed-point equations, i.e., formulae of the form $x \equiv…

Logic in Computer Science · Computer Science 2024-12-06 Tim S. Lyon

Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…

Data Structures and Algorithms · Computer Science 2025-02-20 Eduard Eiben , Tomohiro Koana , Magnus Wahlström

A formal definition of epsilon-complexity of an individual continuous function defined on a unit cube is proposed. This definition is consistent with the Kolmogorov's idea of the complexity of an object. A definition of epsilon-complexity…

Mathematical Physics · Physics 2013-03-08 Boris Darkhovsky , Alexandra Pyriatinska