An accelerated parallel projection method for solving the minimum length problem

Authors

  • D.V. Dolgiy
  • E.A. Nurminski

Keywords:

метод вложенных разбиений
задача проекций
симплекс конечномерного евклидового пространства
параллельный алгоритм
численные методы

Abstract

The problem of determining the minimum-length vector in the simplex of finite-dimensional Euclidean space is considered. A finite accelerated parallel algorithm for solving this problem is proposed.

New computational technologies

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Published

2006-10-30

Issue

Vol. 7 (2006): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

D.V. Dolgiy

Institute of Automation and Control Processes of FEB RAS (IACP FEB RAS)

E.A. Nurminski

Institute of Automation and Control Processes of FEB RAS (IACP FEB RAS)

References

  1. Коннов И.В. Методы решения конечномерных вариационных неравенств. Казань: ДАС, 1998.愦灭;percent-101 с.
  2. Нурминский Е.А. Ускорение итеративных методов проекции на многограннике // Исследовано в России. 2005. 51-62 (http://zhurnal.ape.relarn.ru).
  3. Нурминский Е.А. Метод подходящих аффинных подпространств для проекции на симплекс // ЖВМ и МФ. 2005. 45, № 11. 1996-2004.
  4. Еремин И.И. Противоречивые модели оптимального планирования. М.: Наука, 1988.愦灭;percent-160с.
  5. Wang C., Xiu N. Convergence of the gradient projection method for generalized convex minimization // Computational Optimization and Applications. 2000. 16, № 2. 111-120.
  6. Шпирко С.В., Антипин А.С., Голиков А.И. Равновесное программирование: постановка задачи, методы решения // Информационный бюллетень РФФИ. 1996. T. 4(1). 438.
  7. Zhang J., Xiu N. Some recent advances in projections-type methods for variational inequalities // Journal of Computational and Applied Mathematics. 2003. 152, № 1, 2. 559-585.
  8. Панин В.М., Скопецкий В.В., Лаврина Т.В. Модели и методы конечномерных вариационных неравенств // Кибернетика и системный анализ. 2000. 6. 47-64.
  9. Censor Y., Cohen N., Kutscher (Kotzer) T., Shamir J. Summed squared distance error reduction by simultaneous multiprojections and applications // Applied Mathematics and Computations. 2002. 126. 157-179.
  10. Golub G., Pereyra V. Separable nonlinear least squares: the variable projection method and its applications // Inverse Problems. 2003. 19, № 2. R1- R26.
  11. Нурминский Е.А. Параллельный метод проекции на выпуклую оболочку семейства множеств // Известия ВУЗов. Математика. 2003. 12, № 499. 78-82.
  12. GNU Octave (http://www.octave.org).
Received: 2007-08-27
Accepted: 2007-09-15
Published: 2007-09-26
 How to cite   
Boronina M.A., Vshivkov V.A., Levichev E.B., Snytnikov V.N. et al. An algorithm for the three-dimensional modeling of ultrarelativistic beams // Numerical Methods and Programming. 2007. 8, No 4. 352–359.

TEX CODE:

Boronina M. , Vshivkov V. , Levichev E. et al., (2007) “An algorithm for the three-dimensional modeling of ultrarelativistic beams,” Numerical Methods and Programming, vol. 8, no. 4, pp. 352–359.

TEX CODE:

M. Boronina, V. Vshivkov, E. Levichev et al., “An algorithm for the three-dimensional modeling of ultrarelativistic beams,” Numerical Methods and Programming 8, no. 4 (2007): 352–359

TEX CODE:

Boronina M. , Vshivkov V. , Levichev E. et al. An algorithm for the three-dimensional modeling of ultrarelativistic beams. Numerical Methods and Programming. 2007;8(4):352–359.(In Russ.).

TEX CODE:

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