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Mathematics > Optimization and Control

arXiv:1812.04517 (math)
[Submitted on 11 Dec 2018 (v1), last revised 16 Dec 2018 (this version, v2)]

Title:Some Analogue of Quadratic Interpolation for a Special Class of Non-Smooth Functionals and One Application to Adaptive Mirror Descent for Constrained Optimization Problems

Authors:Fedor S. Stonyakin
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Abstract:Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a possibility of constructing an analogue of such interpolation in the class of locally Lipschitz quasi-convex functionals with the special conditions of non-smoothness (Lipshitz-continuous subgradient) introduced in this paper. As an application, estimates are obtained for the rate of convergence of the previously proposed adaptive mirror descent method for the problems of minimizing a quasi-convex locally Lipschitz functional with several convex functional constraints.
Comments: in Russian
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1812.04517 [math.OC]
  (or arXiv:1812.04517v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.04517

Submission history

From: Fedor Stonyakin [view email]
[v1] Tue, 11 Dec 2018 16:16:31 UTC (12 KB)
[v2] Sun, 16 Dec 2018 10:44:49 UTC (12 KB)
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