Abstract: Firstly, a BB(BarzilaiBorwein)type parameter was used to construct the approximate matrix of the Hessian matrix of the objective function, and the trial step was solved by minimizing the cubic regularized approximation gradient model at the current iteration point. Secondly, a nonmonotone cubic regularization BB algorithm was proposed based on nonmonotone line search strategies. Finally, the convergence of the proposed algorithm was proved. Numerical experiment results show that the numerical performance of the algorithm is good.

Key words: 大规模无约束优化, 梯度算法, BB(BarzilaiBorwein)算法, 三次正则化算法, 非单调线搜索