A New Class of Memory Gradient Methods with Inexact Line Searches

摘要

In this paper we present a new class of memory gradient methods with inexact line searches for unconstrained minimization problems. The methods use more previous iterative information than other methods to generate a search direction and use inexact line searches to select a step-size at each iteration. We prove that the search direction at each iteration satisfies angle property automatically and that the new methods have global convergence under mild conditions. The convergence rate of these methods is also investigated in the case of uniformly convex objective functions. Some numerical experiments show that the new algorithm converges more stably than other line search methods and is effective in solving large scale unconstrained minimization problems.