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Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids

Publication ,  Journal Article
Ahipasaoglu, SD; Sun, P; Todd, MJ
Published in: Optimization Methods and Software
February 1, 2008

We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Using similar techniques, we show the linear convergence of the Frank-Wolfe algorithm with away steps applied to the simplex, under conditions different from those of Gulat and Marcotte. Computational tests confirm the attractive features of this method.

Duke Scholars

Published In

Optimization Methods and Software

DOI

EISSN

1029-4937

ISSN

1055-6788

Publication Date

February 1, 2008

Volume

23

Issue

1

Start / End Page

5 / 19

Related Subject Headings

  • Operations Research
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 4602 Artificial intelligence
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Ahipasaoglu, S. D., Sun, P., & Todd, M. J. (2008). Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optimization Methods and Software, 23(1), 5–19. https://doi.org/10.1080/10556780701589669
Ahipasaoglu, S. D., P. Sun, and M. J. Todd. “Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids.” Optimization Methods and Software 23, no. 1 (February 1, 2008): 5–19. https://doi.org/10.1080/10556780701589669.
Ahipasaoglu SD, Sun P, Todd MJ. Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optimization Methods and Software. 2008 Feb 1;23(1):5–19.
Ahipasaoglu, S. D., et al. “Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids.” Optimization Methods and Software, vol. 23, no. 1, Feb. 2008, pp. 5–19. Scopus, doi:10.1080/10556780701589669.
Ahipasaoglu SD, Sun P, Todd MJ. Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optimization Methods and Software. 2008 Feb 1;23(1):5–19.

Published In

Optimization Methods and Software

DOI

EISSN

1029-4937

ISSN

1055-6788

Publication Date

February 1, 2008

Volume

23

Issue

1

Start / End Page

5 / 19

Related Subject Headings

  • Operations Research
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 4602 Artificial intelligence
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics