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Contracting Proximal Methods for Smooth Convex Optimization · Around

2019

Contracting Proximal Methods for Smooth Convex Optimization

Doikov, Nikita, Nesterov, Yurii

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In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods.

At every step of these methods, we need to minimize a contracted version of the objective function augmented by a regularization term in the form of Bregman divergence.
We provide global convergence analysis for a general scheme admitting inexactness in solving the auxiliary subproblem.
In the case of using for this purpose high-order tensor methods, we demonstrate an acceleration effect for both convex and uniformly convex composite objective functions.

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