# Development of modal interval algorithm for solving continuous minimax problems

 dc.contributor Li, Shuhui dc.contributor Trace, Bruce S. dc.contributor Wang, James L. dc.contributor Zhao, Shan dc.contributor.advisor Sun, Min dc.contributor.author Luo, Xin dc.date.accessioned 2018-01-19T19:38:06Z dc.date.available 2018-01-19T19:38:06Z dc.date.issued 2017 dc.identifier.other u0015_0000001_0002761 dc.identifier.other Luo_alatus_0004D_13164 dc.identifier.uri http://ir.ua.edu/handle/123456789/3399 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 etdms.degree.department University of Alabama. Dept. of Mathematics etdms.degree.discipline Mathematics etdms.degree.grantor The University of Alabama etdms.degree.level doctoral etdms.degree.name Ph.D.
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