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BEAK THEORY AND MODELING
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BEAK THEORY AND MODELING
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Emil Yershov 
Edition
Issue №1
Pages
52-67
Abstract
In a finite-dimensional real space, we consider sets that have a point with both minimum and maximum coordinates on such a set, called its mini - or Maxi-beak, respectively. Conditions sufficient for the existence of sets of beaks are formulated and proved. In systems of inequalities that define such sets, functions are used that are non-increasing or non-decreasing for all arguments except, perhaps, one. Optimization of non-decreasing and non-increasing criteria on a set with a corresponding beak leads to the problem of finding it as a characteristic optimal solution. We introduce the concept of a generalized beak of a set that uses a given quasi-order structure, and consider a sufficient condition for its existence. The dependence of beak coordinates on parameters defining families of sets and the relationship of beaks to solutions of systems of equations is analyzed. A General scheme is proposed for constructing sets that are closed with respect to the introduced binary operations of coordinate minimization and maximization and are used to define sets that have beaks.
Date of publication
01.01.2007
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