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On a Gradient Flow with Exponential Rate of Convergence

Author

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  • Hadi Khatibzadeh

    (University of Zanjan)

Abstract

We present an evolution equation governed by a maximal monotone operator with exponential rate of convergence to a zero of the maximal monotone operator. When the maximal monotone operator is the subdifferential of a convex, proper, and lower semicontinuous function, we show that the trajectory of solutions of the evolution equation converges exponentially to the minimum value of the convex function.

Suggested Citation

  • Hadi Khatibzadeh, 2013. "On a Gradient Flow with Exponential Rate of Convergence," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 141-147, April.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0189-0
    DOI: 10.1007/s10957-012-0189-0
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    References listed on IDEAS

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    1. Hadi Khatibzadeh, 2012. "On the Rate of Convergence of Gradient Flow for Some Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 685-690, August.
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