Guiding iterative optimisation methods to a predefined kind of optima for unconstrained optimisation problems

Abstract

One of the most fundamental issues in the field of mathematical optimisation is the convergence of an iterative optimisation method and by this we are referring to two things. First, will the method find an optimum and second, will this optimum be a local one or a global one? A recently proposed technique (Nikolakakou et al., 2015b) that is used in order to lessen the dependence a locally convergent iterative optimisation method has on the initial guess, is exploited in this paper. A way so that such a method may be guided to a predefined kind of minimum (local or global) is presented. Well known test functions were used for experimentation. Statistical analysis was conducted by applying a logistic regression classification model on data arisen from the numerical results which confirmed that iterative optimisation methods can be guided to a predefined kind of optimum.