Convergence of a quasi-Newton method for solving systems of nonlinear underdetermined equations
研究了一种求解非线性欠定方程组的拟牛顿法，给出了半局部收敛性证明，并在过参数化神经网络监督学习等应用中验证了效果。
Abstract The development and convergence analysis of a quasi-Newton method for the solution of systems of nonlinear underdetermined equations is investigated. These equations arise in many application fields, e.g., supervised learning of large overparameterised neural networks, which require the development of efficient methods with guaranteed convergence. In this paper, a new approach for the computation of the Moore–Penrose inverse of the approximate Jacobian coming from the Broyden update is presented and a semi-local convergence result for a damped quasi-Newton method is proved. The theoretical results are illustrated in detail for the case of systems of multidimensional quadratic equations, and validated in the context of eigenvalue problems and supervised learning of overparameterised neural networks.