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 \alpha_k at each iteration is equal to ۱‎. ‎ 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.