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We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems.
Comput. Math. Math. Phys. 3
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In: Inverse and Ill-posed Problems. deGruyter (2011)
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Devolder, O.: Exactness, inexactness and stochasticity in first-order methods for large-scale convex optimization · 2013
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Mathematical Programming 146
Devolder, O., Glineur, F., Nesterov, Y.: First-order methods of smooth convex optimization with inexact oracle · 2014
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In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 795–811. Springer (2016)
Karimi, H., Nutini, J., Schmidt, M.: Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition · 2016
Optimization Methods and Software 35
Polyak, B., Tremba, A.: New versions of newton method: step-size choice, convergence domain and under-determined equations · 2020
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Acta Numerica 30
Belkin, M.: Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation · 2021
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(in Russian)
Gasnikov, A.V.: In: Modern Numerical Optimization Methods: The Universal Gradient Descent Method. Moscow, MCCME (2021) · 2021
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arXiv preprint arXiv:2102.02921 (2021)
Vasin, A., Gasnikov, A., Spokoiny, V.: Stopping rules for accelerated gradient methods with additive noise in gradient · 2021
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(in Russian)
Vorontsova, E., Hildbrand, R., Gasnikov, A., Stonyakin, F.: Convex optimization (2021) · 2021
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Cited alongside, same era.