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Complexity of finding near-stationary points of convex functions stochastically

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arxiv 1802.08556 v1 pith:PWM4TRY5 submitted 2018-02-21 math.OC

classification math.OC
keywords convexmethodratestochasticsubgradientappliedcomplexitydrives
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abstract

In a recent paper, we showed that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. In this supplementary note, we present a stochastic subgradient method for minimizing a convex function, with the improved rate $\widetilde O(k^{-1/2})$.

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  1. Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints

    math.OC 2019-08 conditional novelty 6.0 of 10

    A proximally constrained subgradient method finds a nearly stationary point for weakly convex objectives with weakly convex constraints in O(1/epsilon^4) deterministic and O~(1/epsilon^6) stochastic iterations.

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