A search algorithm for the minimum location of an unimodal function of several variables (Q2736572)

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.