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Multiple Start Branch and Prune Filtering Algorithm for Nonconvex Optimization

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Algorithmic Foundations of Robotics XII

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 13))

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Abstract

Automatic control systems, electronic circuit design, image registration, SLAM and several other engineering problems all require nonconvex optimization. Many approaches have been developed to carry out such nonconvex optimization, but they suffer drawbacks including large computation time, require tuning of multiple unintuitive parameters and are unable to find multiple local/global minima. In this work we introduce multiple start branch and prune filtering algorithm (MSBP), a Kalman filtering-based method for solving nonconvex optimization problems. MSBP starts off with a number of initial state estimates, which are branched and pruned based on the state uncertainty and innovation respectively. We show that compared to popular methods used for solving nonconvex optimization problems, MSBP has fewer parameters to tune, making it easier to use. Through a case study of point set registration, we demonstrate the efficiency of MSBP in estimating multiple global minima, and show that MSBP is robust to initial estimation error in the presence of noise and incomplete data. The results are compared to other popular methods for nonconvex optimization using standard datasets. Overall MSBP offers a better success rate at finding the optimal solution with less computation time.

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Author information

Authors and Affiliations

  1. Robotics Institute at Carnegie Mellon University, 5000 Forbes avenue, Pittsburgh, PA, 15213, USA

    Rangaprasad Arun Srivatsan & Howie Choset

Authors
  1. Rangaprasad Arun Srivatsan
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  2. Howie Choset
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Corresponding author

Correspondence to Rangaprasad Arun Srivatsan .

Editor information

Editors and Affiliations

  1. Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA

    Ken Goldberg

  2. Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Pieter Abbeel

  3. Rutgers University, Piscataway, NJ, USA

    Kostas Bekris

  4. University of California, Berkeley, CA, USA

    Lauren Miller

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Srivatsan, R.A., Choset, H. (2020). Multiple Start Branch and Prune Filtering Algorithm for Nonconvex Optimization. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_1

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