Lower Rate of Convergence for Locating a Maximum of a Function

Abstract

The problem is considered of estimating the point of global maximum of a function $f$ belonging to a class $F$ of functions on $\lbrack -1, 1 \rbrack,$ based on estimates of function values at points selected possibly during the experimentation. If $p$ is odd and greater than 1, $K$ is a positive constant and $F$ contains enough functions with $p$th derivatives bounded by $K$, then we prove that, under additional weak regularity conditions, the lower rate of convergence is $n^{-(p - 1)/(2p)}$.