Taking the maximum step size is not always beneficial to the convergence of the algorithm especially when the current iterate is far away from the optimal point. It is a common strategy to determine the actual step size by applying a backtracking line-search procedure to explore a decreasing sequence of the step size coefficient with an initial value of 1. In the context of solving the μ-barrier problem in IPM, the filter method, originally proposed by Fletcher and Leyffer [11], is implemented in [8, 9].
is not always beneficial to the convergence of the algorithm especially when the current iterate is far away from the optimal point. It is a common strategy to determine the actual step size by applying a backtracking line-search procedure to explore a decreasing sequence 
with an initial value of 1. 