In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on methods are categorized as line search since they compute a next iterate straight determined by direction which approximates the central path. The proposed uses arc approximation. We discuss convergence properties of algorithm. also conduct numerical e...

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.

We propose two algorithms for nonconvex unconstrained optimization problems that employ Polak-Ribière-Polyak conjugate gradient formula and new inexact line search techniques. We show that the new algorithms converge globally if the function to be minimized has Lipschitz continuous gradients. Preliminary numerical results show that the proposed methods for particularly chosen line search condit...

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...

Data Sources and Searches An experienced medical librarian performed comprehensive literature searches in the electronic data bases Ovid MEDLINE, Ovid Embase, and The Cochrane Library from data base inception to August 15, 2016. The first search was conducted in Ovid MEDLINE. To improve the retrieval of relevant studies and to ensure the methodologic quality of the literature search, an additio...

A global convergence theorem for unconstrained minimization algorithms with an eecient line search is derived. The theorem applies to a new version of the conjugate gradient method derived here in terms of minimizing the eeect of zigzagging. The global convergence condition makes much weaker demands on the line search than previous methods. Local Q-linear convergence in a neighborhood of a stro...