Related papers: A New Linear Programming Method in Sphere Packing
We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear…
In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…
Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of…
A Matlab-based computational procedure is proposed to fill a given volume with spheres whose radii are randomly picked from any specified probability distribution supported by \verb|Matlab|. The general program sequence and examples of…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
In this paper we study the hard sphere packing problem in the Hamming space by the cavity method. We show that both the replica symmetric and the replica symmetry breaking approximations give maximum rates of packing that are asymptotically…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution…
We present an O(mn^2) algorithm for linear programming over the real numbers with n primal and m dual variables through deciding the support set a of an optimal solution. Let z and e be two 2(n+m)-tuples with z representing the primal, dual…
In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding…
Given a set of 2-dimensional (2-D) scattering points, which are usually obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the collected observations. However, some of…
Proximal methods such as the Alternating Direction Method of Multipliers (ADMM) are effective at solving constrained quadratic programs (QPs). To tackle infeasible QPs, slack variables are often introduced to ensure feasibility, which…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…