Towards Pure Adaptive Search

Abstract

-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 functions the gap is bridged. .. Keywords AbstractThe 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 comple.xity, 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 functions the gap is \)ridged.

On the Investigation of Stochastic Global Optimization Algorithms

“…The relevance for the concept of convergence speed are due to the analyses by Zabinsky and Smith [13] and Baritompa et al [1], who show that a fixed success rate of an effective algorithm in the sense of uniform covering would lead to an algorithm which is polynomial in the dimension of the problem, i.e. the expected number of function evaluations grows polynomially with the dimension of the problem.…”