A Retrospective Adaptive Cubic Regularisation Method For Unconstrained Optimization

We propose a retrospective adaptive cubic regularization method for unconstrained optimization, which is based on the similarity of updating between the trust region radius and the regularization parameter. The method is established by combining the idea presented by Bastin et al [ Mathematical Programming,2010,123(2),395-418] with the algorithm by Cartis et al [Part Ⅰ:Mathematical Programming,2011,127(2),245-295]. Under reasonable assumptions, we can prove its global convergence. Nu-merical tests show that our algorithm needs less number of iterations than the original algorithm for some test problems.