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

Document Type : Research Paper


Department of Mathematics, Yazd University, P. O. Box 89195-74, Yazd, Iran


‎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 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.