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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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