A New Conjugate Gradient Trust Region Method and its Convergence

Conjugate gradient methods are widely used for large scale unconstrained optimization. A new class of conjugate gradient trust region method is proposed, in which trust region technique is used for guaranteeing the global convergence of the algorithm, and more utilizable information on conjugate gradient vectors is used for accelerating convergence of the algorithm. The global convergence, super linear convergence and quadratic convergence properties of the algorithm are proved under favorable conditions, respectively. Numerical experiments show that the new algorithm is robust and effective.