The Use of Quadratic Regularization with a Cubic Descent Condition for Unconstrained Optimization
本文证明了一种带三次充分下降条件的二次正则化方法，在最坏情况下能达到与三次正则化和信赖域方法相同的一阶和二阶复杂度，并给出了渐近收敛性和收敛阶结果。
Cubic-regularization and trust-region methods with worst-case first-order complexity $O(\varepsilon^{-3/2})$ and worst-case second-order complexity $O(\varepsilon^{-3})$ have been developed in the last few years. In this paper it is proved that the same complexities are achieved by means of a quadratic-regularization method with a cubic sufficient-descent condition instead of the more usual predicted-reduction based descent. Asymptotic convergence and order of convergence results are also presented. Finally, some numerical experiments comparing the new algorithm with a well-established quadratic regularization method are shown.