Open AccessAn Evolutionary Approach to Constructing the Minimum Volume Ellipsoid Containing a Set of Points and the Maximum Volume Ellipsoid Embedded in a Set of Points
Author(s) -
Rewayda Abo-Alsabeh,
Abdellah Salhi
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1530/1/012087
Subject(s) - ellipsoid , volume (thermodynamics) , set (abstract data type) , ellipsoid method , mathematics , combinatorics , mathematical optimization , computer science , algorithm , geometry , physics , convex optimization , quantum mechanics , regular polygon , convex combination , programming language , astronomy
Given a set of points C = { x 1 , x 2 , …, x m } ⊆ R n , what is the minimum volume ellipsoid that encloses it? Equally interestingly, one may ask: What is the maximum volume ellipsoid that can be embedded in the set of points without containing any? These problems have a number of applications beside being interesting in their own right. In this paper we review the important results concerning these and suggest an evolutionary-type approach for their solution. We will also highlight computational results.