Sensitivity Analysis of Merit Function in Solving Nonlinear Equations by Optimization

Seyyed Shahabeddin Azimi, Mansour Kalbasi () and Hamidreza Sadeghifar
Additional contact information
Seyyed Shahabeddin Azimi: Amirkabir University of Technology
Mansour Kalbasi: Amirkabir University of Technology
Hamidreza Sadeghifar: Simon Fraser University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 1, No 10, 201 pages

Abstract: Abstract To solve nonlinear equations by an optimization method, scaling is very important. Two types of poor scaling where: (a) the variables differ greatly in magnitude; (b) the merit function of system is highly sensitive to small changes in certain variables and relatively insensitive to changes in other variables. If poor scaling is ignored, the algorithm may produce solutions with poor quality. To solve (a), we can change units of variables. A numerical solution of the nonlinear equations produced by the finite volume method in the forced convective heat transfer of a nanofluid, as a case study, indicates that the poor scaling (b) is solved by using the Euclidean norm of columns of the Jacobian matrix as scaling data, while some researchers proposed diagonal elements of the Hessian matrix as scaling data.

Keywords: Nonlinear equations; Optimization; Merit function; Scaling matrix; Jacobian (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0439-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0439-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-013-0439-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().