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In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz (PL) inequality.
USSR Computational Mathematics and Mathematical Physics 3
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Mathematical Programming 116
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Mathematics of Operations Research 35
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Mathematical Programming 145
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Optimization Letters 11
De Klerk, E., Glineur, F., Taylor, A.B.: On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions · 2017
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Mathematical Programming 161
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Necoara, I., Nesterov, Y., Glineur, F.: Linear convergence of first order methods for non-strongly convex optimization · 2019
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In: Conference on Learning Theory, pp. 1894–1938. PMLR (2020)
Hinder, O., Sidford, A., Sohoni, N.: Near-optimal methods for minimizing star-convex functions and beyond · 2020
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Optimization Letters pp. 1–13 (2021)
Abbaszadehpeivasti, H., de Klerk, E., Zamani, M.: The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions · 2021
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arXiv preprint arXiv:2109.13566 (2021)
Abbaszadehpeivasti, H., de Klerk, E., Zamani, M.: On the rate of convergence of the difference-of-convex algorithm (DCA) · 2021
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Mathematical Programming 187
Hu, B., Seiler, P., Lessard, L.: Analysis of biased stochastic gradient descent using sequential semidefinite programs · 2021
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arXiv preprint arXiv:2203.07305 (2022)
Gupta, S.D., Van Parys, B.P., Ryu, E.K.: Branch-and-bound performance estimation programming: A unified methodology for constructing optimal optimization methods · 2022
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