Convergence of descent method without line search

Abstract

Line search method is sometimes a useful and efficient technique for solving unconstrained optimization problems, especially for solving small and middle scale problems. However, A line search procedure is necessary at each iteration, leading to a significant amount of computation. In order to reduce the evaluations of objective functions and gradients, the line search procedure should be avoided in algorithm design. In this paper we propose a new descent method without line search for unconstrained optimization problems. The algorithm is required to estimate some parameters at each iteration. We analyze theoretically the global convergence of the new algorithm under mild conditions. These theoretical conclusions can help us in designing new efficient methods for optimization problems.