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Mathematics > Functional Analysis

arXiv:1807.00387 (math)
[Submitted on 1 Jul 2018 (v1), last revised 22 Nov 2018 (this version, v3)]

Title:Convergence rates for an inertial algorithm of gradient type associated to a smooth nonconvex minimization

Authors:Szilárd Csaba László
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Abstract:We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the generated sequences converge to a critical point of the objective function, if a regularization of the objective function satisfies the Kurdyka-Łojasiewicz property. Further, we provide convergence rates for the generated sequences and the function values formulated in terms of the Łojasiewicz exponent.
Comments: 24 pages
Subjects: Functional Analysis (math.FA)
MSC classes: 90C26, 90C30, 65K10
Cite as: arXiv:1807.00387 [math.FA]
  (or arXiv:1807.00387v3 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1807.00387

Submission history

From: Szilárd László Ph.D. [view email]
[v1] Sun, 1 Jul 2018 20:00:26 UTC (17 KB)
[v2] Thu, 19 Jul 2018 14:00:20 UTC (18 KB)
[v3] Thu, 22 Nov 2018 12:13:19 UTC (18 KB)
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