Hesitant adaptive search for global optimisation

Pure adaptive search is a stochastic algorithm which has been analysed in distinct ways for finite and continuous global optimisation. In this paper, motivated by the behaviour of practical algorithms such as simulated annealing, we extend these ideas. We present a unified theory which yields both the finite and continuous results for pure adaptive search. At the same time, we allow our extended algorithm to "hesitate" before improvement continues. Results are obtained for the expected number of iterations to convergence for such an algorithm.