A Branch and Bound algorithm for multidimensional Holder optimization: Estimation of the age-dependent viral hepatitis A infection force

Abstract

In the present framework, we develop a branch and bound multidimensional Holder optimization method. This method is composed of two subroutines. The first one allows converting the multivariate objective function into a single variable one using the alpha-dense space fitting curves. In the second subroutine, we minimize the single variable function resulting from the first subroutine. To achieve this task, we develop a novel iterative optimization method reducing the feasible region in each iteration taking into account the property of Holder of the objective function. We apply this method to solve a parameters identification problem resulting from the modelling of the spread of viral hepatitis A in the central west of Tunisia following the increase in the number of infections. The Tunisian health authorities wanted to know the prevalence and the infection force of the virus in order to identify the situation and take the necessary measures. The modelling leads to a minimization problem of the least square multivariate error between the observed values and the theoretical ones. Besides, we implement the proposed method in some numerical experiments to evaluate its efficiency.