Full convergence of the steepest descent method with inexact line searches
- 1 January 1995
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 32 (2) , 137-146
- https://doi.org/10.1080/02331939508844042
Abstract
Several finite procedures for determining the step size of the steepest descent method for unconstrained optimization, without performing exact one-dimensional minimizations, have been considered in the literature. The convergence analysis of these methods requires that the objective function have bounded level sets and that its gradient satisfy a Lipschitz condition, in order to establish just stationarity of all cluster points. We consider two of such procedures and prove, for a convex objective, convergence of the whole sequence to a minimizer without any level set boundedness assumption and, for one of them, without any Lipschitz condition.Keywords
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