Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Solution of linear programming and non-linear regression problems using linear M-estimation methods
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
1999 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to algorithms for solving two optimization problems, using linear M-estimation methods, and their implementation. First, an algorithm for the non-linear M-estimation problem is considered. The main idea of the algorithm is to linearize the residual function in each iteration and thus calculate the iteration step by solving a linear M- estimation problem. A 2-norm bound on the variables restricts the step size, to guarantee convergence. The other algorithm solves the dual linear programming problem by making a ``smooth'' approximation of edges and inequality constraints using quadratic functions, thus making it possible to use Newton's method to find the optimal solution. The quadratic approximation of the inequality constraint makes it a penalty function algorithm. The implementation uses sparse matrix techniques. Since it is an active set method, it is possible to reuse the old factor when calculating the new step, by up- and downdating the old factor. It is only occasionally, when the downdating fails, that the factor instead has to be found with a sparse multifrontal LQ-factorization.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1999. , 117 p.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544 ; 1999:17
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:ltu:diva-26286Local ID: d8097200-763a-11db-962b-000ea68e967bOAI: oai:DiVA.org:ltu-26286DiVA: diva2:999448
Note
Godkänd; 1999; 20061117 (haneit)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-24Bibliographically approved

Open Access in DiVA

fulltext(2231 kB)15 downloads
File information
File name FULLTEXT01.pdfFile size 2231 kBChecksum SHA-512
3bb144aea041b00e9682035040c4a3a032cd4260accaa1f38b2503a4b17889a84a41726829179f78f8be5e39d1bbbb2afc0710818340c358e43e6fbe5d61fd54
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Edlund, Ove
By organisation
Mathematical Science
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 15 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 50 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf