Nonmonotone Curvilinear Line Search Methods for Unconstrained Optimization

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semidefinite is a exhibited for this class of algorithms by means of a nonmonotone stabilization strategy. An implementation using the Bunch-Parlett decomposition is shown to outperform several other techniques on a large class of test problems

Nonmonotone Curvilinear Line Search Methods for Unconstrained Optimization

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semidefinite is exhibited for this class of algorithms by means of a nonmonotone stabilization strategy. An implementation using the Bunch-Parlett decomposition is shown to outperform several other techniques on a large class of test problems. 1 Introduction In this work we consider the unconstrained minimization problem min x2IR n f(x); where f is a real valued function on IR n . We assume throughout that both the gradient g(x) := rf(x) and the Hessian matrix H(x) := r 2 f(x) of f exist and are continuous. Many iterative methods for solving this problem have been proposed; they are usually descent methods that generate a sequence fx k g su..