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A Fast Bilinear Optimization Algorithm
Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media. (FSCN - Fibre Science and Communication Network)
Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.ORCID iD: 0000-0002-0665-1889
2004 (English)In: Proceedings of the Third International Conference on Nonlinear Analysis and Convex Analysis 2003 (NACA 2003), Yokohama: Yokohama Publishers , 2004Conference paper, (Refereed)
Abstract [en]

Computational decision analysis methods (such as DELTA) have been developed and implemented over a number of years for solving decision problems when vague and numerically imprecise information prevails. However, the evaluation phases in those methods often give rise to bilinear programming problems, which are time-consuming to solve in an interactive environment with general nonlinear programming solvers such as SNOPT. This paper proposes a linear programming based algorithm for solving this type of problems, thus enabling interactive use of such methods.

Place, publisher, year, edition, pages
Yokohama: Yokohama Publishers , 2004.
Keyword [en]
linear program, bilinear program, interval probability, utility theory, decision analysis
National Category
Computer Science
Identifiers
URN: urn:nbn:se:miun:diva-1707Local ID: 356ISBN: 4-946552-15-4 (print)OAI: oai:DiVA.org:miun-1707DiVA: diva2:26739
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2009-07-10Bibliographically 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 Science
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: 2009-07-13Bibliographically approved

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