A derivative free multidimensional optimal search method using Lucas number

摘要

We consider a unimodal continuous function of N variables over an N-dimensional rectangular parallelopiped and explain a search method to find the domain of uncertainty which contains the point that maximizes the function. Our search method does not require differentiability assumption. The function is projected along each dimension. An algorithm is developed to eliminate the subset of the domain at each step, which does not contain the solution. Lucas numbers are used in the elimination process.