Accession Number : AD0714175
Title : Interval Analysis in Control: Extreme Points of Interval Functions.
Descriptive Note : Technical rept.,
Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
Personal Author(s) : Ihara,S. ; Jacobson,D. H.
Report Date : SEP 1970
Pagination or Media Count : 43
Abstract : The paper presents some basic mathematical properties of the extreme points of a class of interval functions. A minimum of the upper bound function or a maximum of the lower bound function of an interval function can be considered, respectively, as a Min-Max or a Max-Min solution of a simple two players' game where the objective function is linear in the first player's variables. The main difference from the classic Min-Max theory exists in the simultaneous consideration of both Min-Max and Max-Min solutions. The first player's optimization is replaced with interval arithmetic at the sacrifice of the tightness of the bound functions, and a systematic and straightforward procedure to obtain the directional derivatives of the resultant functions is presented. Most properties are proved on the basis of interval arithmetic though some of them follow from the Min-Max theory. (Author)
Descriptors : (*FUNCTIONS(MATHEMATICS), OPTIMIZATION), GAME THEORY, SET THEORY, PARTIAL DIFFERENTIAL EQUATIONS, MINIMAX TECHNIQUE
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE