Related papers: Semidefinite and linear programming bounds for sum…
A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and show that each such program can be solved by a computer to bound the…
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric.…
There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P. In a breakthrough paper Fiorini et al. [Proceedings of 44th ACM Symposium on Theory of Computing 2012,…
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on…
In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
The concept of \emph{data depth} in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. \emph{Halfspace depth} is a measure of data depth. Given a set $S$ of points…
In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
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…
Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances [javanmard et al., 2016]. Given…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions, with an emphasis on SDP relaxations for polynomial optimization problems. This approach incorporates the inexact augmented…
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…
In this paper we give a randomized reduction for the Rank Syndrome Decoding problem and Rank Minimum Distance problem for rank codes. Our results are based on an embedding from linear codes equipped with Hamming distance unto linear codes…