Volume 21, No 3, 2014, P. 87-102

UDC 519.85
G. Sh. Tamasyan and A. A. Chumakov
Finding the distance between the ellipsoids

Abstract:
The problem of finding the nearest points between two ellipsoids is considered. New algorithms for solving this problem were constructed using the theory of exact penalty functions and nonsmooth analysis. We propose two iterative methods of (steepest and hypodifferential) descent. New algorithms (as compared with previously known) have specific advantages, in particular, they are universal and less labor-intensive. The software which implements these algorithms was developed in MATLAB and Maple environment.
Bibliogr. 12.

Keywords: nonsmooth analysis, nearest distance, ellipsoid, exact penalty, subdifferential, method of hypodifferential descent.

Tamasyan Grigoriy Shalikovich ¹
Chumakov Andrey Alexandrovich ¹
1. St. Petersburg State University,
35 Universitetskiy Ave., 198504 Peterhof, St. Petersburg, Russia
e-mail: grigoriytamasjan@mail.ru, katandrew@mail.ru