Abstract
This is a survey of the recent researches on the global complexity bounds of the gradient methods and the Newton-type methods for the nonlinear programming problem. The classical benchmarks of these iterative methods, such as global convergence and rates of convergence, do not represent a total computational time. The global complexity bound is the worst number of iterations to find an appropriate solution, and hence it is proportional to the worst computational time. In recent years the global complexity bounds of the gradient methods and the Newton-type methods have been vigorously investigated. In the survey we report some of these results.
