Smooth minimization of non-smooth functions
(2005) Mathematical Programming — Vol. 103, n° 1, p. 127-152 (2005)
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- Abstract
- In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization. From the viewpoint of efficiency estimates, we manage to improve the traditional bounds on the number of iterations of the gradient schemes from 0 (1/e2) to 0 (1/e), keeping basically the complexity of each iteration unchanged.
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Nesterov, Y. (2005). Smooth minimization of non-smooth functions. Mathematical Programming, 103(1), 127-152. https://doi.org/10.1007/s10107-004-0552-5 (Original work published 2005)