Unconstrained Convex Minimization in Relative Scale

CORE Discussion Paper No. 2003/96

20 Pages Posted: 23 Apr 2007

See all articles by Yurii Nesterov

Yurii Nesterov

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Date Written: December 2003

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 δ in at most e · √m(2 + lnm) · (1 + 1 δ ) iterations of a gradient-type scheme, where m is the largest dimension of the problem and e is the Euler number.

Keywords: nonlinear optimization, convex optimization, complexity bounds, relative accuracy, fully polynomial approximation schemes, gradient methods, optimal methods

Suggested Citation

Nesterov, Yurii, Unconstrained Convex Minimization in Relative Scale (December 2003). CORE Discussion Paper No. 2003/96, Available at SSRN: https://ssrn.com/abstract=981384 or http://dx.doi.org/10.2139/ssrn.981384

Yurii Nesterov (Contact Author)

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
1348 Louvain-la-Neuve, 1348
Belgium

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