Convergence and Stability of Line Search Methods for Unconstrained Optimization
This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search method to be globally asymptotical stable. Our analysis suggests that the proposed sufficient conditions for asymptotical stability is equivalent to the Zoutendijk-type conditions in conventional global convergence analysis.
line search methods unconstrained optimization global convergence lyapunov stability globally asymptotical stability 65k05 49k40