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Improved Cutting Plane Methods for Disjoint Bilinear Programming
Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media. (FSCN - Fibre Science and Communication Network)
(English)Manuscript (preprint) (Other academic)
Keyword [en]
linear programming, bilinear programming, non-convex programming, cutting plane, branch and bound, underestimation, global optimization
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:miun:diva-6268Local ID: 3061OAI: oai:DiVA.org:miun-6268DiVA: diva2:31307
Available from: 2009-02-18 Created: 2009-02-18 Last updated: 2018-01-12Bibliographically approved
In thesis
1. Bilinear optimization in computational decision analysis
Open this publication in new window or tab >>Bilinear optimization in computational decision analysis
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In real-life decision analysis, significant recognition has been given to theunrealistic expectation of numerically precise information. Many modernapproaches attempting to handle imprecision have focused more on representationand less on evaluation. The DELTA method, as one of the fewleading approaches, challenges this issue by its evaluation framework thatcan accommodate both precision and imprecision. However, computationally,DELTA and similar approaches may incur time-consuming calculationsdue to the introduction of imprecise information concerning probability andutility. In general, those problems are bounded non-convex bilinear optimizationprograms with disjoint linear constraints, which cannot be solvedeffectively by any existing general-purpose global optimization technique.This thesis presents two enhanced cutting plane algorithms for solvingbounded disjoint bilinear programs arising in computational decision analysis.Each algorithm consists of a local phase designed to determine a localoptimizer from an approximate solution, and a global phase designed to systematicallyexplore the feasible region, subset by subset. These two phasesare switched automatically during the global search procedure. The basicframework builds upon previously developed efficient cutting plane methods.By embedding the lower bounding technique in a branch and bound procedure,the improvement of their performances seems encouraging in the lightof computational experience. Even though the motivation to develop thesealgorithms stems from computational decision analysis, the idea can also beextended to the development of optimization approaches for handling generalbounded disjoint bilinear programs, especially for larger sized ones.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2005
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 2
National Category
Information Systems
Identifiers
urn:nbn:se:miun:diva-8856 (URN)
Public defence
2005-05-27, O102, Åkroken, Sundsvall, 13:15 (English)
Opponent
Supervisors
Available from: 2009-05-06 Created: 2009-05-06 Last updated: 2018-01-13Bibliographically approved

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Ding, Xiaosong

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CiteExportLink to record
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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
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