基于三次模型的线搜索方法及其收敛性

A Line Search Method with Cubic Model and It's Convergence Property

针对无约束优化问题,给出一种基于三次模型的线搜索型算法,并在适当的条件下证明算法的全局收敛性.该算法以对称矩阵代替原三次模型中的Hessian阵,并且不需要保持正定和Dennis-Moré条件,它与一般线搜索法不同,在每次迭代中步长可以在下降方向上由显性公式直接确定,从而可以减少搜索计算.

A line search method with conic model for unconstrained optimization was proposed,and its global convergence result was proved under some suitable conditions.In the cubic model of the algorithm,the Hessian matrix of the objective function is replaced by a symmetric matrix without the positive definite assumption and the Dennis-Moré condition.At each iteration,the step-size is computed by an explicit formula on the descent direction which is different from general line search methods so that the search computation can be simplified.