Network structure of the set of local minima in optical system optimization

Florian Bociort; Eco van Driel; Alexander Serebriakov

doi:10.1117/12.504522

6 November 2003 Network structure of the set of local minima in optical system optimization

Florian Bociort, Eco van Driel, Alexander Serebriakov

Proceedings Volume 5174, Novel Optical Systems Design and Optimization VI; (2003) https://doi.org/10.1117/12.504522
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

We discuss a surprising new feature of the merit function landscape in optical system design. When certain conditions are satisfied, the set of local minima forms a network in which all nodes are connected. Each link between two neighboring minima contains a special type of saddle point (more precisely, a saddle point having a Morse index. On this basis, a new global optimization method that takes advantage of this feature is proposed. The central component of the new method, the algorithm for saddle point detection, works in a parameter space of arbitrary dimensionality, and uses only the local optimization engine of the optical design program. For a simple global optimization search (the symmetric Cooke triplet) the network of the corresponding set of local minima is presented.

Citation Download Citation

Florian Bociort, Eco van Driel, and Alexander Serebriakov "Network structure of the set of local minima in optical system optimization", Proc. SPIE 5174, Novel Optical Systems Design and Optimization VI, (6 November 2003); https://doi.org/10.1117/12.504522

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