有奇异解的无约束最优化问题的一种混合法

A HYBRID METHOD FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEM WITH SINGULAR SOLUTIONS

本文研究求解含有奇异解的无约束最优化问题算法 .该类问题的一个重要特性是目标函数的Hessian阵可能处处奇异 .我们提出求解该类问题的一种梯度 -正则化牛顿型混合算法 .并在一定的条件下得到了算法的全局收敛性 .而且 ,经一定迭代步后 ,算法还原为正则化 Newton法 .因而 ,算法具有局部二次收敛性 .

In this paper, we propose a hybrid method for unconstraint minimization problem with singular solutions. An essential feature of the problem lies in that the Hessian matrix of the objective function may be singular everywhere. We show that under appropriate conditions, the proposed hybrid method is globally convergent. Moreover, after a finite number of iterations, the hybrid method reduces to the regularized Newton method. Consequently, it possesses locally quadratic convergence property.