TR2020-088

Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability


    •  Romero, O., Benosman, M., "Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability", International Journal of Control, June 2020.
      BibTeX TR2020-088 PDF
      • @article{Romero2020jun2,
      • author = {Romero, Orlando and Benosman, Mouhacine},
      • title = {Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability},
      • journal = {International Journal of Control},
      • year = 2020,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2020-088}
      • }
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  • Research Area:

    Optimization

In this paper we propose a new family of continuous-time optimization algorithms based on discontinuous second order gradient optimization flows, with finite-time convergence guarantees to local optima, for locally strongly convex (time-varying) cost functions. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of (time-varying) differential inclusions. We then prove the convergence of these second-order flows in finite-time. In some particular cases, we can show that the finite-time convergence can be pre-defined by the user. We propose a robustification of the flows to bounded additive uncertainties, and extend some of the results to the case of constrained optimization. We show the performance of these flows on well-know optimization benchmarks, namely, the Rosenbrock function, and the Rastringin function.

 

  • Related Publication

  •  Romero, O., Benosman, M., "Robust Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability", World Congress of the International Federation of Automatic Control (IFAC), August 2020.
    BibTeX TR2020-120 PDF
    • @inproceedings{Romero2020aug,
    • author = {Romero, Orlando and Benosman, Mouhacine},
    • title = {Robust Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability},
    • booktitle = {World Congress of the International Federation of Automatic Control (IFAC)},
    • year = 2020,
    • month = aug,
    • url = {https://www.merl.com/publications/TR2020-120}
    • }