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The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Optimization and Control · Mathematics 2025-11-24 Danqing Zhou , Hongmei Chen , Shiqian Ma , Junfeng Yang

In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…

Statistics Theory · Mathematics 2025-05-28 Rushil Mallarapu , Mark Sellke

The aim of this paper is to highlight recent progress in using conic optimization methods to study geometric packing problems. We will look at four geometric packing problems of different kinds: two on the unit sphere -- the kissing number…

Optimization and Control · Mathematics 2025-10-09 Frank Vallentin

Let $\Gamma=\Gamma(A)$ denote a simple strongly connected digraph with vertex set $X$, diameter $D$, and let $\{A_0,A:=A_1,A_2,\ldots,A_D\}$ denote the set of distance-$i$ matrices of $\Gamma$. Let $\{R_i\}_{i=0}^D$ denote a partition of…

Combinatorics · Mathematics 2024-04-08 Giusy Monzillo , Safet Penić

The graphical realization of a given degree sequence and given partition adjacency matrix simultaneously is a relevant problem in data driven modeling of networks. Here we formulate common generalizations of this problem and the Exact…

Combinatorics · Mathematics 2021-12-15 Eva Czabarka , Laszlo A. Szekely , Zoltan Toroczkai , Shanise Walker

We study the asymptotic behaviour of sequences of integral functionals depending on moving anisotropies. We introduce and describe the relevant functional setting, establishing uniform Meyers-Serrin type approximations, Poincar\'e…

Analysis of PDEs · Mathematics 2025-04-04 Alberto Maione , Fabio Paronetto , Simone Verzellesi

The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…

Optimization and Control · Mathematics 2015-11-25 Edwin R. van Dam , Renata Sotirov

The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…

Optimization and Control · Mathematics 2021-07-07 Franz Rendl , Renata Sotirov , Christian Truden

The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…

Numerical Analysis · Mathematics 2014-04-08 Pierre Degond , Alexei Lozinski , Jacek Narski , Claudia Negulescu

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

Machine Learning · Computer Science 2019-03-05 Azade Nazi , Will Hang , Anna Goldie , Sujith Ravi , Azalia Mirhoseini

The random sequential adsorption of various particle shapes is studied in order to determine the influence of particle anisotropy on the saturated random packing. For all tested particles there is an optimal level of anisotropy which…

Materials Science · Physics 2015-10-28 Michał Cieśla , Grzegorz Pająk , Robert M. Ziff

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Romina Gaburro

We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…

Computational Geometry · Computer Science 2025-05-27 Jiaqi Zheng , Tiow-Seng Tan

Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…

Analysis of PDEs · Mathematics 2024-06-25 Jules Candau-Tilh

We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…

Optimization and Control · Mathematics 2017-05-25 Beniamin Bogosel

In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^2(\Omega) \leq C \delta(\Omega)$ where $\delta$ is the isoperimetric deficit and $\lambda_0$ is the barycentric asymmetry. Our aim is to…

Optimization and Control · Mathematics 2021-07-23 Chiara Bianchini , Gisella Croce , Antoine Henrot

This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric…

General Relativity and Quantum Cosmology · Physics 2019-03-27 Milko Estrada , Francisco Tello-Ortiz

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…

Numerical Analysis · Mathematics 2018-07-30 Assyr Abdulle , Andrea Di Blasio

On an orientable surface $S$, consider a collection $\Gamma$ of closed curves. The (geometric) intersection number $i_S(\Gamma)$ is the minimum number of self-intersections that a collection $\Gamma'$ can have, where $\Gamma'$ results from…

Computational Geometry · Computer Science 2024-02-08 Loïc Dubois

We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…

Analysis of PDEs · Mathematics 2017-05-02 Gabriel Deugoue , Jean Louis Woukeng