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

Journal article (2009)
Department
Imaging Science and Technology (AS) (TU Delft)
Copyright: © 2009 Optical Society of America
DOI: https://doi.org/doi:10.1364/OE.17.006436
Mathematical methods (general) Geometric optical design Lens system design Computation methods
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Published Date

02-04-2009

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Source:

Optics Express, 17 (8), 2009

ISSN:

1094-4087

Source:

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6436

Faculty

Applied Sciences

Department

Imaging Science and Technology

Abstract

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.