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Smooth minimization of non-smooth functions. (English) Zbl 1079.90102
Summary: In this paper we propose a new approach for constructing efficient schemes for non-smooth convex optimization. It is based on a special smoothing technique, which can be applied to 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 $$O(\frac1{\varepsilon^2})$$ to $$O(\frac 1\varepsilon)$$, keeping basically the complexity of each iteration unchanged.

##### MSC:
 90C25 Convex programming 90C60 Abstract computational complexity for mathematical programming problems 49J52 Nonsmooth analysis
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##### References:
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