Development of modal interval algorithm for solving continuous minimax problems

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dc.contributor Li, Shuhui
dc.contributor Trace, Bruce S.
dc.contributor Wang, James L.
dc.contributor Zhao, Shan
dc.contributor.advisor Sun, Min Luo, Xin 2018-01-19T19:38:06Z 2018-01-19T19:38:06Z 2017
dc.identifier.other u0015_0000001_0002761
dc.identifier.other Luo_alatus_0004D_13164
dc.description Electronic Thesis or Dissertation
dc.description.abstract While 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.
dc.format.extent 65 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Development of modal interval algorithm for solving continuous minimax problems
dc.type thesis
dc.type text University of Alabama. Dept. of Mathematics Mathematics The University of Alabama doctoral Ph.D.

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