Towards Pure Adaptive Search

The algorithm known as Pure Adaptive Search is a global optimisation ideal with desirable complexity. In this paper we temper it to a framework we term Somewhat Adaptive Search. This retains the desirable complexity, but allows scope for a practical realisation. We introduce a new algorithm termed Pure Localisation Search which attempts to reach the practical ideal. For a certain class of one variable functions the gap is bridged.

[1]  Robert L. Smith,et al.  Simulated annealing for constrained global optimization , 1994, J. Glob. Optim..

[2]  Robert L. Smith,et al.  Improving Hit-and-Run for global optimization , 1993, J. Glob. Optim..

[3]  P. Basso Iterative Methods for the Localization of the Global Maximum , 1982 .

[4]  B. Shubert A Sequential Method Seeking the Global Maximum of a Function , 1972 .

[5]  Pierre Hansen,et al.  Global optimization of univariate Lipschitz functions: I. Survey and properties , 1989, Math. Program..

[6]  Pierre Hansen,et al.  Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison , 1989, Math. Program..

[7]  Regina Hunter Mladineo An algorithm for finding the global maximum of a multimodal, multivariate function , 1986, Math. Program..

[8]  G. R. Wood,et al.  Multidimensional bisection applied to global optimisation , 1991 .

[9]  Robert L. Smith,et al.  Pure adaptive search in global optimization , 1992, Math. Program..

[10]  Aleksei G. Sukharev,et al.  On adaptive and nonadaptive stochastic and deterministic algorithms , 1990, J. Complex..

[11]  S. A. Piyavskii An algorithm for finding the absolute extremum of a function , 1972 .

[12]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[13]  W. Baritompa,et al.  Customizing methods for global optimization-a geometric viewpoint , 1993, J. Glob. Optim..

[14]  Robert L. Smith,et al.  Pure adaptive search in monte carlo optimization , 1989, Math. Program..

[15]  Graham R. Wood,et al.  The bisection method in higher dimensions , 1992, Math. Program..