论文标题
具有结构化对角线黑森近似的迭代算法，用于解决非线性最小二乘问题
Iterative algorithm with structured diagonal Hessian approximation for solving nonlinear least squares problems
论文作者
论文摘要
非线性最小二乘问题是一类特殊的无约束优化问题，它们的梯度和黑森具有特殊的结构。在本文中，我们利用了这些结构，并提出了一种具有对角线Hessian近似值的无基质算法来解决非线性最小二乘问题。我们制定了适当的保障策略，以确保在整个迭代过程中，黑森州矩阵是积极的。所提出的算法会产生下降方向，并且是全球收敛的。初步数值实验表明，该提出的方法具有最近开发的类似方法的竞争力。
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a diagonal Hessian approximation for solving nonlinear least-squares problems. We devise appropriate safeguarding strategies to ensure the Hessian matrix is positive definite throughout the iteration process. The proposed algorithm generates descent direction and is globally convergent. Preliminary numerical experiments show that the proposed method is competitive with a recently developed similar method.
