A logarithmic barrier approach via majorant function for nonlinear programming

In this paper, we are interested in solving an optimization nonlinear programming problem using a logarithmic barrier interior point method, in which the penalty term is taken as a vector $ r \in \mathbb{R}^{n}_{+} $. The descent direction has been calculated using a classical Newton method, however the step size has been calculated with a new technique of majorant functions and a secant technique. The numerical simulations show us the efficiency of our approach compared to the classical line search method.