A Hybrid Algorithm for Practical Nonconvex Optimization

This paper proposes a hybrid algorithm for optimization, to ensure convergence to a local minimimzer of a nonconvex Morse objective function L with a single, scalar argument. Developed using hybrid system tools, and based on the heavy ball method, the algorithm features switching strategies to detec...

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Bibliographic Details
Published in:IFAC-PapersOnLine 2021-01, Vol.54 (9), p.630-635
Main Authors: Hustig-Schultz, Dawn M., Sanfelice, Ricardo G.
Format: Article
Language:English
Subjects:
algorithms
Hybrid systems
Optimization
Stability
theory
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Summary:This paper proposes a hybrid algorithm for optimization, to ensure convergence to a local minimimzer of a nonconvex Morse objective function L with a single, scalar argument. Developed using hybrid system tools, and based on the heavy ball method, the algorithm features switching strategies to detect whether the state is near a critical point and enable escape from local maximizer, using measurements of the gradient of L. Key properties of the resulting closed-loop system, including existence of solutions and practical global attractivity, are revealed. Numerical results validate the findings.
ISSN:2405-8963
2405-8963
DOI:10.1016/j.ifacol.2021.06.165