Development of modal interval algorithm for solving continuous minimax problems

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dc.contributorLi, Shuhui
dc.contributorTrace, Bruce S.
dc.contributorWang, James L.
dc.contributorZhao, Shan
dc.contributor.advisorSun, Min
dc.contributor.authorLuo, Xin
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2018-01-19T19:38:06Z
dc.date.available2018-01-19T19:38:06Z
dc.date.issued2017
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractWhile there are a large variety of effective methods developed for solving more traditional minimization problems, much less success has been reported in solving the minimax problem $\displaystyle\min_{u \in U}\displaystyle\max_{v \in V}f(u,v)$ where $U\times V$ is a fixed domain in $\mathbb{R}^n$. Most of the existing work deal with a discrete $V$ or even a finite $V$. Continuous minimax problems can be applied to engineering, finance and other fields. Sainz in 2008 proposed a modal interval algorithm based on their semantic extensions to solve continuous minimax problems. We developed an improved algorithm using modal intervals to solve unconstrained continuous minimax problems. A new interval method is introduced by taking advantage of both the original minimax problem and its dual problem. After theoretical analysis of major issues, the new algorithm is implemented in the framework of uniform partition of the search domain. Various improvement techniques including more bisecting choices, sampling methods and deletion conditions are applied to make the new method more powerful. Preliminary numerical results provide promising evidence of its effectiveness.en_US
dc.format.extent65 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0002761
dc.identifier.otherLuo_alatus_0004D_13164
dc.identifier.urihttp://ir.ua.edu/handle/123456789/3399
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleDevelopment of modal interval algorithm for solving continuous minimax problemsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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