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 Hes...
In this note we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the object...
In this paper, a primal dual method for general possible nonconvex nonlinear optimization problems is considered. The method is an exterior point type method which means that it p...
We give the first complete theoretical convergence analysis for the iterative extensions of the Sturm/Triggs algorithm. We show that the simplest extension, SIESTA, converges to no...
Several different uses of Newton's method in connection with the Fundamental Theorem of Algebra are pointed out. Theoretical subdivision schemes have been combined with the n...