Newton's iterates can converge to non-stationary points

Abstract In this note we discuss the convergence of Newton's method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

• Type: Journal
• Year: 2008
• Where: MP
• Authors: Walter F. Mascarenhas
• Keywords: Book Practical Methods, MP 2008, Positive Definite, Wolfe Conditions