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.
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This research was in part supported by a grant from University of Zanjan (No. 9048).
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Communicated by Viorel Barbu.
This research was in part supported by a grant from university of Zanjan (No. 9048). The author would like to thank the referees for valuable comments.
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Khatibzadeh, H. On a Gradient Flow with Exponential Rate of Convergence. J Optim Theory Appl 157, 141–147 (2013). https://doi.org/10.1007/s10957-012-0189-0
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DOI: https://doi.org/10.1007/s10957-012-0189-0