Related papers: A maximal energy pointset configuration problem
This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of…
We study a discrete analogue of the parametric Plateau problem in a non-polynomial tensor-product surface spaces generated by the generalized trigonometric (GT)--B\'ezier basis. Boundary interpolation is imposed by prescribing the boundary…
We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
This work presents a general framework for the operationally driven optimal siting and sizing of battery energy storage systems in power transmission networks, aimed at enhancing their resource adequacy. The approach considers multi-period…
Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…
We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…
Let $\Delta$ be the optimal packing density of $\mathbb R^n$ by unit balls. We show the optimal packing density using two sizes of balls approaches $\Delta + (1 - \Delta) \Delta$ as the ratio of the radii tends to infinity. More generally,…
We consider two related problems: the first is the minimization of the "Coulomb renormalized energy" of Sandier-Serfaty, which corresponds to the total Coulomb interaction of point charges in a uniform neutralizing background (or rather…
Given a set of points in the plane, the \textsc{General Position Subset Selection} problem is that of finding a maximum-size subset of points in general position, i.e., with no three points collinear. The problem is known to be ${\rm…
Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of…
This letter proposes an energy efficient distributed worst case robust power allocation in massive multiple input multiple output (MIMO) system. We assume a bounded channel state information (CSI) error and all channels lie in some bounded…
The average distance of the equal hard spheres is introduced to evaluate the density of a given arrangement. The absolute smallest value is two radii because the spheres can not be closer to each other than their diameter. The absolute…
We consider the problem of optimal location of a Dirichlet region in a $d$-dimensional domain $\Omega$ subjected to a given right-hand side $f$ in order to minimize some given functional of the configuration. While in the literature the…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
We establish robust exponential convergence for $rp$-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} which is stronger than the usual energy norm associated with…
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…