A new trust region dogleg method for unconstrained optimization

Abstract

This paper presents a new trust region dogleg method for unconstrained optimization. The method can deal with the case when the Hessian B of quadratic models is indefinite. It is proved that the method is globally convergent and has a quadratic convergence rate if B (k) = ▿2 f(x (k)). Under certain conditions, the solution obtained by the method is even a second order stationary point. Numerical results also declare effectiveness of the method.