, Volume 26, Issue 2, pp 190-212

Truncated-newtono algorithms for large-scale unconstrained optimization

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We present an algorithm for large-scale unconstrained optimization based onNewton's method. In large-scale optimization, solving the Newton equations at each iteration can be expensive and may not be justified when far from a solution. Instead, an inaccurate solution to the Newton equations is computed using a conjugate gradient method. The resulting algorithm is shown to have strong convergence properties and has the unusual feature that the asymptotic convergence rate is a user specified parameter which can be set to anything between linear and quadratic convergence. Some numerical results on a 916 vriable test problem are given. Finally, we contrast the computational behavior of our algorithm with Newton's method and that of a nonlinear conjugate gradient algorithm.

This research was supported in part by DOT Grant CT-06-0011, NSF Grant ENG-78-21615 and grants from the Norwegian Research Council for Sciences and the Humanities and the Norway-American Association.
This paper was originally presented at the TIMS-ORSA Joint National Meeting, Washington, DC, May 1980.