The Kissing Number Problem: A New Result from Global Optimization

2004 ◽  
Vol 17 ◽  
pp. 203-207 ◽  
Author(s):  
Leo Liberti ◽  
Nelson Maculan ◽  
Sergei Kucherenko
Keyword(s):  
Global Optimization ◽  
Kissing Number ◽  
Number Problem

scholarly journals A Combinatorial Approach to Small Ball Inequalities for Sums and Differences

2018 ◽  
Vol 28 (1) ◽  
pp. 100-129 ◽  
Author(s):  
JIANGE LI ◽  
MOKSHAY MADIMAN
Keyword(s):  
Hilbert Spaces ◽  
Vector Spaces ◽  
Combinatorial Approach ◽  
Kissing Number ◽  
Small Ball ◽  
Small Ball Probabilities ◽  
Packing Problems ◽  
Number Problem ◽  
Probabilistic Inequalities ◽  
Independent Identically Distributed

Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent, identically distributed random elements taking values in very general sets. Depending on the setting – abelian or non-abelian groups, or vector spaces, or Banach spaces – we provide a collection of inequalities relating different small ball probabilities that are sharp in many cases of interest. We prove these distribution-free probabilistic inequalities by showing that underlying them are inequalities of extremal combinatorial nature, related among other things to classical packing problems such as the kissing number problem. Applications are given to moment inequalities.

scholarly journals New formulations for the Kissing Number Problem

2007 ◽  
Vol 155 (14) ◽  
pp. 1837-1841 ◽  
Author(s):  
Sergei Kucherenko ◽  
Pietro Belotti ◽  
Leo Liberti ◽  
Nelson Maculan
Keyword(s):  
Kissing Number ◽  
Number Problem

Global Optimization

1993 ◽  
Author(s):  
Reiner Horst ◽  
Hoang Tuy
Keyword(s):  
Global Optimization

Probability Models in Global Optimization

Informatica ◽  
2016 ◽  
Vol 27 (2) ◽  
pp. 323-334 ◽  
Author(s):  
James M. Calvin
Keyword(s):  
Global Optimization ◽  
Probability Models

Hybrid orthogonal CMAES for solving global optimization problems

2013 ◽  
Vol 32 (4) ◽  
pp. 981-985
Author(s):  
Ya-fei HUANG ◽  
Xi-ming LIANG ◽  
Yi-xiong CHEN
Keyword(s):  
Global Optimization ◽  
Optimization Problems
Sign in / Sign up

Export Citation Format

Share Document