Related papers: Three-point bounds for energy minimization
Physical design problems, such as photonic inverse design, are typically solved using local optimization methods. These methods often produce what appear to be good or very good designs when compared to classical design methods, but it is…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…
We prove the first, even super-polynomial, lower bounds on the size of tropical (min,+) and (max,+) circuits approximating given optimization problems. Many classical dynamic programming (DP) algorithms for optimization problems are pure in…
We prove that the hexagonal lattice is a local minimizer, among all point configurations, of the interaction energy per unit volume for pair potentials that are completely monotonic functions of the square distance. This includes Gaussian…
We revisit the linear programming bounds for the size vs. distance trade-off for binary codes, focusing on the bounds for the almost-balanced case, when all pairwise distances are between $d$ and $n-d$, where $d$ is the code distance and…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…
In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension.
For a set $Q$ of points in the plane and a real number $\delta \ge 0$, let $\mathbb{G}_\delta(Q)$ be the graph defined on $Q$ by connecting each pair of points at distance at most $\delta$. We consider the connectivity of…
Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries…
We give improved lower bounds for binary $3$-query locally correctable codes (3-LCCs) $C \colon \{0,1\}^k \rightarrow \{0,1\}^n$. Specifically, we prove: (1) If $C$ is a linear design 3-LCC, then $n \geq 2^{(1 - o(1))\sqrt{k} }$. A design…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum…
We prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a…