In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require the calculation of a Hessian matrix. They also require fewer deflations than for applying the deflated Newton method on the first order optimality conditions, as the latter finds all stationary points, not just local minima. One application of interest covered in this paper is the inverse eigenvalue problem (IEP) associated with the modelling of spectroscopic data of relevance to the physical and chemical sciences. Open source MATLAB code is provided at https://github.com/AlbanBloorRiley/DeflatedGaussNewton.

翻译：本文推广紧缩技术，提出两种系统性寻找非线性最小二乘问题多个局部极小值的新方法。这些方法基于高斯-牛顿算法，因此无需计算海森矩阵。相较于在一阶最优性条件上应用紧缩牛顿法（该方法会找到所有驻点而不仅是局部极小值），本方法所需的紧缩操作次数更少。本文涵盖的一个重要应用是与物理和化学科学相关的光谱数据建模所对应的逆特征值问题。开源MATLAB代码发布于https://github.com/AlbanBloorRiley/DeflatedGaussNewton。