Truncated-newtono algorithms for large-scale unconstrained optimization |
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Authors: | Ron S Dembo Trond Steihaug |
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Institution: | (1) School of Organization and Management, Yale University, 06520 New Haven, CT, USA;(2) Department of Mathematical Sciences, Rice University, 77001 Houston, TX, USA |
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Abstract: | 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. |
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Keywords: | Unconstrained Optimization Modified Newton Methods Conjugate Gradient Algorithms |
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