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Derivation of Coordinate Descent Algorithms from Optimal Control Theory

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  • Isaac M. Ross

    (Naval Postgraduate School)

Abstract

Recently, it was posited that disparate optimization algorithms may be coalesced in terms of a central source emanating from optimal control theory. Here we further this proposition by showing how coordinate descent algorithms may be derived from this emerging new principle. In particular, we show that basic coordinate descent algorithms can be derived using a maximum principle and a collection of max functions as “control” Lyapunov functions. The convergence of the resulting coordinate descent algorithms is thus connected to the controlled dissipation of their corresponding Lyapunov functions. The operational metric for the search vector in all cases is given by the Hessian of the convex objective function.

Suggested Citation

  • Isaac M. Ross, 2023. "Derivation of Coordinate Descent Algorithms from Optimal Control Theory," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:2:d:10.1007_s43069-023-00215-6
    DOI: 10.1007/s43069-023-00215-6
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    References listed on IDEAS

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    1. B. S. Goh, 1997. "Algorithms for Unconstrained Optimization Problems via Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 581-604, March.
    2. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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