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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6436–6450

Chaotic behavior in an algorithm to escape from poor local minima in lens design

Maarten van Turnhout and Florian Bociort  »View Author Affiliations

Optics Express, Vol. 17, Issue 8, pp. 6436-6450 (2009)

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In lens design, damped least-squares methods are typically used to find the nearest local minimum to a starting configuration in the merit function landscape. In this paper, we explore the use of such a method for a purpose that goes beyond local optimization. The merit function barrier, which separates an unsatisfactory solution from a neighboring one that is better, can be overcome by using low damping and by allowing the merit function to temporarily increase. However, such an algorithm displays chaos, chaotic transients and other types of complex behavior. A successful escape of the iteration trajectory from a poor local minimum to a better one is associated with a crisis phenomenon that transforms a chaotic attractor into a chaotic saddle. The present analysis also enables a better understanding of peculiarities encountered with damped least-squares algorithms in conventional local optimization tasks.

© 2009 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(220.2740) Optical design and fabrication : Geometric optical design
(220.3620) Optical design and fabrication : Lens system design
(080.1753) Geometric optics : Computation methods

ToC Category:
Optical Design and Fabrication

Original Manuscript: February 17, 2009
Revised Manuscript: March 24, 2009
Manuscript Accepted: April 1, 2009
Published: April 2, 2009

Maarten van Turnhout and Florian Bociort, "Chaotic behavior in an algorithm to escape from poor local minima in lens design," Opt. Express 17, 6436-6450 (2009)

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