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18 September 2007 Predictability and unpredictability in optical system optimization
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Local optimization algorithms, when they are optimized only for speed, have in certain situations an unpredictable behavior: starting points very close to each other lead after optimization to different minima. In these cases, the sets of points, which, when chosen as starting points for local optimization, lead to the same minimum (the so-called basins of attraction), have a fractal-like shape. Before it finally converges to a local minimum, optimization started in a fractal region first displays chaotic transients. The sensitivity to changes in the initial conditions that leads to fractal basin borders is caused by the discontinuous evolution path (i.e. the jumps) of local optimization algorithms such as the damped-least-squares method with insufficient damping. At the cost of some speed, the fractal character of the regions can be made to vanish, and the downward paths become more predictable. The borders of the basins depend on the implementation details of the local optimization algorithm, but the saddle points in the merit function landscape always remain on these borders.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Maarten van Turnhout and Florian Bociort "Predictability and unpredictability in optical system optimization", Proc. SPIE 6667, Current Developments in Lens Design and Optical Engineering VIII, 666709 (18 September 2007);


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