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Relative effectiveness of the trust-region algorithm with precise secund order derivatives

Kőházi-Kis, Ambrus (2019) Relative effectiveness of the trust-region algorithm with precise secund order derivatives. GRADUS, 6 (1). pp. 1-7. ISSN 2064-8014

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Abstract

Trust-region methods with precise Hessian matrix have some drawbacks: time consuming calculation of the elements of the second order derivative matrix, and the generally non-definite Hessian matrix causes numerical and methodical troubles. Their applicability depends on how well their substitute, for example the Levenberg-Marguardt-method performs. The Levenberg- Marguardt-method often performs well in least-sguares prob- lems. This procedure dynamically mixes the steepest-descent and the Gauss-Newton-methods. Generally one hopes that the more analytical properties of the problems cost function utilized in an optimization procedure, the faster, the more effective search method can be constructed. It is definitely the case when we use first derivatives together with function values (instead of just func- tion values). In the case of second derivatíve of the cost function the situation is not so clear. In lot of cases even if second order model is used within the search procedure the Hessian matrix is just approximated, and it is not calculated precisely even if it would be possible to calculate analytically, because of its tem- poral cost and a big amout of memory needed. in this paper I investigate whether the precise Hessian matrix is worth to be determined, whether one gains more on the increased effective- ness of the search method than looses on the increased tempo- ral costof dealing with the precise Hessian matrix. In this paper it is done by the comparison of the Levenberg-Marguardt-method and a trust-region method using precise Hessian matrix.

Item Type: Article
Uncontrolled Keywords: Levenberg-Marquardt-method, Trust-region method, Hessian matrix, Eigen-value problem, Numerical stability
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Zoltán Subecz
Date Deposited: 08 Jun 2020 14:18
Last Modified: 08 Jun 2020 14:18
URI: http://real.mtak.hu/id/eprint/109378

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