Interval Newton/generalized bisection when there are singularities near roots (Q1173718)

The paper considers the use of interval Newton methods in conjunction with generalized bisection for finding the global optimum, within a specified box, of a twice differentiable function. Modifications are proposed to make the generalized bisection method work more efficiently when the Hessian matrix of the given function is either ill-conditioned or singular at the optimum. Some numerical experiments are reported.