This article is cited in 78 papers

Deterministic Systems

Gradient methods for nonstationary unconstrained optimization problems

A. Yu. Popkov

Institute of Systems Analysis, Russian Academy of Sciences, Moscow, Russia

Abstract: Problems of unconstrained optimization with an objective function depending on a scalar parameter (time) are considered. The solution of these problems also depends on time and any numerical method must keep track of this dependence. For the solution of such nonstationary problems, a discrete gradient method is treated, in which only one gradient step is taken for the varying function at each instant of time. Estimates of intervals (variations) between exact and approximate solutions are found and an asymptotic behavior of these estimates is defined.

Presented by the member of Editorial Board: B. T. Polyak

Received: 17.01.2005

 English version: Automation and Remote Control, 2005, 66:6, 883–891

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