Unconstrained convex minimization in relative scale

Yu Nesterov

No 2003096, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: nonlinear optimization; convex optimization; complexity bounds; relative accuracy; fully polynomial approximation schemes; gradient methods; optimal methods (search for similar items in EconPapers)
Date: 2003-12
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Citations: View citations in EconPapers (3)

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