Multilevel dichotomy algorithm in global optimization

Global Optimization in Action

“…This generalization is based on the dimensionality-free convergence investigations of Chapter 2.2: for this reason, the approach is essentially independent of the original one-dimensional function class models which served as the basis of the corresponding univariate global optimization algorithms. It should be noted at this point that diverse, more specific generalizations and diverse extensions of Piyavskii's univariate algorithm are discussed, for example, by Mayne and Polak (1984), Galperin (1985Galperin ( , 1987Galperin ( , 1988, Mladineo (1986Mladineo ( , 1992a, Strigul (1987), Nefedov (1987), Shepilov (1987), Mayne (1988, 1989), Korotkich (1989), Wood (1991Wood ( , 1992 and Zhang, Wood and Baritompa (1993). Additionally, semi-heuristic multivariate extensions of one-dimensional statistical function models are reviewed and discussed, for example, by Mockus (1989) and Zilinskas (1982Zilinskas ( , 1992.…”

Algorithms for multi-extremal mathematical programming problems employing the set of joint space-filling curves

“…One of the recent approaches to global optimization (see, e.g., Butz (1968), Strongin (1973)) is based on the idea of reducing the initial multi-dimensional multi-extremal optimization problems to equivalent one-dimensional problems using classical Peano-space-filling curves (some alternative approaches are viewed, for example, in Evtushenko (1985), Horst (1990), Korotkich (1989), Pinter (1988), Rinnooy Kan and Timmer (1989)). Numerical methods for the arising problem of computing this type of map are described in Butz (1971), Strongin (1978Strongin ( , 1990 and in Gergel et al (1987).…”