Correlation and realization of quasi-Newton methods of absolute optimization

Sviridenko A.B., Zelenkov G.A.
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Newton and quasi-Newton methods of absolute optimization based on Cholesky factorization with adaptive step and finite difference approximation of the first and the second derivatives. In order to raise effectiveness of the quasi-Newton methods a modified version of Cholesky decomposition of quasi-Newton matrix is suggested. It solves the problem of step scaling while descending, allows approximation by non-quadratic functions, and integration with confidential neighborhood method. An approach to raise Newton methods effectiveness with finite difference approximation of the first and second derivatives is offered. The results of numerical research of algorithm effectiveness are shown.

Keywords: Newton methods, quasi-Newton methods, Cholesky factorization, step scaling, method of confidence neighborhoods, finite difference approximation, algorithm, numerical research, absolute optimization
Citation in English: Sviridenko A.B., Zelenkov G.A. Correlation and realization of quasi-Newton methods of absolute optimization // Computer Research and Modeling, 2016, vol. 8, no. 1, pp. 55-78
Citation in English: Sviridenko A.B., Zelenkov G.A. Correlation and realization of quasi-Newton methods of absolute optimization // Computer Research and Modeling, 2016, vol. 8, no. 1, pp. 55-78
DOI: 10.20537/2076-7633-2016-8-1-55-78
URL: http://crm-en.ics.org.ru/journal/article/2411/

 

Supplementary information:

 

Application KNmbm – software implementation of quasi-Newton optimization methods with step regulation, based on the Cholesky factorization. The algorithm is implemented in the Visual Basic .NET language, development environment is Microsoft Visual Studio 2010. Options quasi-Newton methods: symmetric rank-one formula, BFGS, DFP, PSB.

KNMBM.zip

 

 

Application KNmbmApp – software implementation of quasi-Newton optimization methods with step regulation, based on the Cholesky factorization. KNmbmApp different from its classical prototype KNmbm finite-difference approximation of the first derivatives. The algorithm is implemented in the Visual Basic .NET language, development environment is Microsoft Visual Studio 2010. Options quasi-Newton methods: symmetric rank-one formula, BFGS, DFP, PSB.

KNMBMApp.zip

 

 

Application Nmbm (Sviridenko A.B. Certificate №2015610399 from 01.12.2015) – a software implementation of Newton optimization methods with step regulation, based on the Cholesky factorization. The algorithm is implemented in the Visual Basic .NET language, development environment is Microsoft Visual Studio 2010.

NMBM.zip

 

 

Application NmbmApp (A.B. Sviridenko, G.A. Zelenkov Certificate №2015610347 of 01.12.2015) – a software implementation of Newton optimization methods with step regulation, based on the Cholesky factorization. NmbmApp different from its classical prototype Nmbm (Sviridenko A.B. Certificate №2015610399 from 01.12.2015) finite-difference approximation of the first and second derivatives. The algorithm is implemented in the Visual Basic .NET language, development environment is Microsoft Visual Studio 2010.

NMBMApp.zip

 

 

 

Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Anastasiya Borisovna Sviridenko. Direct multiplicative methods for sparse matrices. Newton methods. // Computer Research and Modeling. — 2017. — V. 9, no. 5. — P. 679. DOI: 10.20537/2076-7633-2017-9-5-679-703
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