A search algorithm for the minimum location of an unimodal function of several variables
The function \(J(u)\) is called unimodal on the interval \(U= [a, b]\) if there exist numbers \(\alpha, \beta\) \((a\leq\alpha\leq\beta\leq)\) such that: NEWLINENEWLINENEWLINE1) \(J(u)\) is a stricly monotonously decreasing function for \(a\leq u\leq \alpha\) (if \(\alpha < a)\); NEWLINENEWLINENEWLINE2) \(J(u)\) is a stricly monotonously increasing function for \(\beta \leq u \leq b\) (if \(\beta < b)\); NEWLINENEWLINENEWLINE3) \(J(u) = J_{*} = \inf_{u \in U} J(u)\) for \(\alpha \leq u \leq \beta.\) NEWLINENEWLINENEWLINEThe notion of unimodal function is generalized to the case of unimodal functions of several variables and an search algorithm for the minimum of the functions is given.
scientific article; zbMATH DE number 1644400