Optimally conditioned optimization algorithms without line searches View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1975-12

AUTHORS

William C. Davidon

ABSTRACT

New variable metric algorithms are presented with three distinguishing features:They make no line searches and allow quite arbitrary step directions while maintaining quadratic termination and positive updates for the matrixH, whose inverse is the hessian matrix of second derivatives for a quadratic approximation to the objective function.The updates fromH toH+ are optimally conditioned in the sense that they minimize the ratio of the largest to smallest eigenvalue ofH−1H+.Instead of working with the matrixH directly, these algorithms represent it asJJT, and only store and update the Jacobian matrix J. A theoretical basis is laid for this family of algorithms and an example is given along with encouraging numerical results obtained with several standard test functions. They make no line searches and allow quite arbitrary step directions while maintaining quadratic termination and positive updates for the matrixH, whose inverse is the hessian matrix of second derivatives for a quadratic approximation to the objective function. The updates fromH toH+ are optimally conditioned in the sense that they minimize the ratio of the largest to smallest eigenvalue ofH−1H+. Instead of working with the matrixH directly, these algorithms represent it asJJT, and only store and update the Jacobian matrix J. A theoretical basis is laid for this family of algorithms and an example is given along with encouraging numerical results obtained with several standard test functions. More... »

PAGES

1-30

References to SciGraph publications

Journal

TITLE

Mathematical Programming

ISSUE

1

VOLUME

9

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01681328

DOI

http://dx.doi.org/10.1007/bf01681328

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020786346


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