A batch, derivative-free algorithm for finding multiple local minima
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We propose a derivative-free algorithm for finding high-quality local minima for functions that require significant computational resources to evaluate. Our algorithm efficiently utilizes the computational resources allocated to it and also has strong theoretical results, almost surely starting a finite number of local optimization runs and identifying all local minima. We propose metrics for measuring how efficiently an algorithm finds local minima, and we benchmark our algorithm on synthetic problems (with known local minima) and two real-world applications.
KeywordsDerivative-free optimization Multistart Parallel algorithms Global optimization
Mathematics Subject Classification90C56 90C30 90C26
We are grateful to Maria Rudnaya and Aswin Kannan for coding the microscopy problem and to Christine Shoemaker for valuable discussions on multistart methods.
- Finkel D (2003) DIRECT. URL: http://www4.ncsu.edu/~ctk/Finkel_Direct/Direct.m
- Rudnaya ME, Kho SC, Mattheij RMM, Maubach JML (2010) Derivative-free optimization for autofocus and astigmatism correction in electron microscopy. In: Proceedings of the 2nd International Conference on Engineering Optimization, 1–10. Lisbon, Portugal. http://www.dem.ist.utl.pt/engopt2010/Book_and_CD/Papers_CD_Final_Version/pdf/06/01059-01.pdf
- Wild SM (2009) Derivative-free optimization algorithms for computationally expensive functions. Ph.D. thesis, Cornell University. URL:http://ecommons.cornell.edu/handle/1813/11248Google Scholar