Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained opti...

We describe several line search strategies in recent potential reduction algorithms for linear programming. We clarify some concerns about the step size of the original algorithm. In particular, we illustrate that the dual step of the algorithm can be suuciently \long". We also discuss some other implementation issues for the algorithm.

Hydrocephalus is a neurological disease which causes ventricular dilation due to abnormalities in the cerebrospinal fluid (CSF) circulation. Although treatment via a CSF shunt in the brain ventricles has been performed, poor rates of patient responses continue. Thus, to aid surgeons in hydrocephalus treatment planning, we propose a geometric computational approach for tracking hydrocephalus ven...