Convergence of line search methods for unconstrained optimization

Abstract

Line search methods are traditional and successful methods for solving unconstrained optimization problems. Its convergence has attracted more attention in recent years. In this paper we analyze the general results on convergence of line search methods with seven line search rules. It is clarified that the search direction plays a main role in these methods and that step-size guarantees the global convergence in some cases. It is also proved that many line search methods have same convergence property. These convergence results can enable us to design powerful, effective, and stable algorithms in practice. Finally, a class of special line search methods is investigated.