Unconstrained convex minimization in relative scale

Nesterov, Yurii
(2003)

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  • Nesterov, YuriiUCLouvain
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Abstract
In this paper we present a new approach to constructing schemes for unconstrained convex minimization, which compute approximate solutions with a certain relative accuracy. This approach is based on a special conic model of the unconstrained minimization problem. Using a structural model of the objective function we can employ the efficient smoothing technique. The fastest of our algorithms solves a linear programming problem with relative accuracy [delta] in at most e. sq.m(2 + lnm).(1 + 1 /[delta]) iterations of a gradient-type scheme, where m is the largest dimension of the problem and e is the Euler number.
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Nesterov, Y. (2003). Unconstrained convex minimization in relative scale (CORE Discussion Papers 2003/96). https://hdl.handle.net/2078.5/33737