Global minimization algorithms for Hölder functions (Q1599138)

The one-dimensional global optimization problem \(\min\{f(x):x\in [a,b]\}\) is considered where the function \(f(x)\) satisfies the Hölder condition \(|f(x)- f(y)|\leq h|x-y|^{1/N}\). A new scheme for the method of \textit{S. A. Piyavskij} [U.S.S.R. Comput Math. Math. Phys. 12(1972), No. 4, 57-67 (1973; Zbl 0282.65052)] is proposed and three algorithms are given. Numerical tests are presented.