The newton bracketing method for convex minimization: Convergence analysis

Abstract

Let f be a convex function bounded below with infimum fmin attained. A bracket is an interval [L,U] containing fmin. The Newton Bracketing (NB) method for minimizing f, introduced in [Levin and Ben-Israel, Comput. Optimiz. Appl. 21, 213–229 (2002)], is an iterative method that at each iteration transforms a bracket [L,U] into a strictly smaller bracket [L+,U+] with L ≤ L+