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Sparse solutions of optimal control via Newton method for under-determined systems

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Listed:
  • Boris Polyak

    (Institute for Control Sciences)

  • Andrey Tremba

    (Institute for Control Sciences)

Abstract

We focus on finding sparse and least-$$\ell _1$$ℓ1-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined equations can be applied successively for such problems.

Suggested Citation

  • Boris Polyak & Andrey Tremba, 2020. "Sparse solutions of optimal control via Newton method for under-determined systems," Journal of Global Optimization, Springer, vol. 76(3), pages 613-623, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00784-z
    DOI: 10.1007/s10898-019-00784-z
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    References listed on IDEAS

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    1. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yurii, 2007. "Gauss-Newton scheme with worst case guarantees for global performance," LIDAM Reprints CORE 1952, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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