无约束优化的非单调三次正则BB算法

Non-monotone Cubic Regularization BB Algorithm for Unconstrained Optimization

先利用BB(Barzilai-Borwein)类型参数构造目标函数Hessian矩阵的近似矩阵,通过极小化当前迭代点处的三次正则化近似梯度模型求解试探步,再结合非单调线搜索策略提出一个非单调三次正则BB算法,最后给出算法的收敛性证明.数值实验结果表明,该算法数值性能良好.

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.