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Primal-dual subgradient methods for minimizing uniformly convex functions
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abstract
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are adaptive with respect to the parameters of strong or uniform convexity of the objective: in the case when the total number of iterations $N$ is fixed, their accuracy coincides, up to a logarithmic in $N$ factor with the accuracy of optimal algorithms.
Forward citations
Cited by 2 Pith papers
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A constructive approach to strengthen algebraic descriptions of function and operator classes
A constructive one-point strengthening procedure derives stricter, often semidefinite-representable necessary conditions for extending functions and operators from finite data.
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Restart schemes for SGD on KL-satisfying non-smooth weakly convex problems deliver accelerated convergence robust to exponent misspecification, with optimal schedules resembling Polyak steps.
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