scholarly journals New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming

2006 ◽  
Vol 113 (8) ◽  
pp. 1719-1731 ◽  
Author(s):  
Dion Gijswijt ◽  
Alexander Schrijver ◽  
Hajime Tanaka
Keyword(s):  
Semidefinite Programming ◽  
Upper Bounds ◽  
Terwilliger Algebra ◽  
Nonbinary Codes

scholarly journals Upper bounds for packings of spheres of several radii

2014 ◽  
Vol 2 ◽  
Author(s):  
DAVID DE LAAT ◽  
FERNANDO MÁRIO DE OLIVEIRA FILHO ◽  
FRANK VALLENTIN
Keyword(s):  
Linear Programming ◽  
Euclidean Space ◽  
Semidefinite Programming ◽  
Unit Sphere ◽  
Upper Bound ◽  
Convex Bodies ◽  
Classical Problem ◽  
Upper Bounds ◽  
Sphere Packings ◽  
Spherical Caps

AbstractWe 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 for packings of spherical caps and of convex bodies through the use of semidefinite programming. We perform explicit computations, obtaining new bounds for packings of spherical caps of two different sizes and for binary sphere packings. We also slightly improve the bounds for the classical problem of packing identical spheres.

scholarly journals Improving the UWB Pulseshaper Design Using Nonconstant Upper Bounds in Semidefinite Programming

2007 ◽  
Vol 1 (3) ◽  
pp. 396-404 ◽  
Author(s):  
Christian R. Berger ◽  
Michael Eisenacher ◽  
Shengli Zhou ◽  
Friedrich K. Jondral
Keyword(s):  
Semidefinite Programming ◽  
Upper Bounds

scholarly journals Defining quantum divergences via convex optimization

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 387
Author(s):  
Hamza Fawzi ◽  
Omar Fawzi
Keyword(s):  
Convex Optimization ◽  
Semidefinite Programming ◽  
Quantum Channel ◽  
Upper Bounds ◽  
Chain Rule ◽  
Quantum Channels ◽  
Optimization Program ◽  
Rényi Divergence ◽  
Strong Converse ◽  
A Chain

We introduce a new quantum Rényi divergence Dα# for α∈(1,∞) defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum Rényi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwiched α-Rényi divergence between quantum channels for α>1. Second it allows us to prove a chain rule property for the sandwiched α-Rényi divergence for α>1 which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.

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