An efficient improvement of the Newton method for solving nonconvex optimization problems

‎Newton method is one of the most famous numerical methods among the line search methods to minimize functions. It is well known that the search direction and step length play important roles in this class of methods to solve optimization problems. In this investigation, a new modification of the Newton method to solve unconstrained optimization problems is presented. The significant merit of the proposed method is that the step length αk at each iteration is equal to 1. Additionally, the convergence analysis for this iterative algorithm is established under suitable conditions. Some illustrative examples are provided to show the validity and applicability of the presented method and a comparison is made with several other existing methods.