A corrector–predictor interior-point method with new search direction for linear optimization

Abstract

We introduce a feasible corrector–predictor interior-point algorithm (CP IPA) for solving linear optimization problems which is based on a new search direction. The search directions are obtained by using the algebraic equivalent transformation (AET) of the Newton system which defines the central path. The AET of the Newton system is based on the map that is a difference of the identity function and square root function. We prove global convergence of the method and derive the iteration bound that matches best iteration bounds known for these types of methods. Furthermore, we prove the practical efficiency of the new algorithm by presenting numerical results. This is the first CP IPA which is based on the above mentioned search direction.