An inexact line search approach using modified nonmonotone strategy for unconstrained optimization

This paper concerns with a new nonmonotone strategy and its application to the line search approach for unconstrained optimization. It has been believed that nonmonotone techniques can improve the possibility of finding the global optimum and increase the convergence rate of the algorithms. We first introduce a new nonmonotone strategy which includes a convex combination of the maximum function value of some preceding successful iterates and the current function value. We then incorporate the proposed nonmonotone strategy into an inexact Armijo‐type line search approach to construct a more relaxed line search procedure. The global convergence to first‐order stationary points is subsequently proved and the R‐linear convergence rate are established under suitable assumptions. Preliminary numerical results finally show the efficiency and the robustness of the proposed approach for solving unconstrained nonlinear optimization problems.