AI 中文总结
该研究针对受非线性和线性约束的非线性最小二乘问题，提出算法，通过将目标重述为增广拉格朗日函数处理非线性约束，用梯度投影技术近似求解线性约束问题，还涉及海森矩阵近似，展示全局收敛性并经实验评估性能。
AI 中文摘要
我们提出了一种算法来解决受非线性和线性约束混合影响的非线性最小二乘问题。非线性约束通过将目标重新表述为增广拉格朗日函数来处理，而线性约束直接处理。每次迭代包括通过梯度投影技术近似求解一个线性约束问题。我们的方法还涉及增广拉格朗日海森矩阵的结构化近似。我们展示了该方法的全局收敛性，并通过数值实验评估了性能。
英文摘要
We present an algorithm for solving nonlinear least-squares problems subject to a mix of nonlinear and linear constraints. The nonlinear constraints are handled by reformulating the objective as the augmented Lagrangian function while linear constraints are handled directly. Each iteration consists of approximately solving a linearly constrained problem by means of a gradient projection technique. Our approach also involves a structured approximation of the augmented Lagrangian Hessian. We show global convergence of the method and assess the performance through numerical experiments.
