We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse problems, but the cost of assembling and factorizing the associated matrices has so far been a major stumbling block. In this work, we show how the dense Gauss-Newton Hessian can be transformed into an equivalent sparse matrix that can be assembled and factorized much more efficiently. This leads to drastically reduced computation times for many inverse problems, which we demonstrate on a diverse set of examples. We furthermore show links between sensitivity analysis and nonlinear programming approaches based on Lagrange multipliers and prove equivalence under specific assumptions that apply for our problem setting.

中文翻译：

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SGN：用于加速灵敏度分析的稀疏 Gauss-Newton

我们提出了一种稀疏高斯-牛顿求解器，用于加速灵敏度分析，并应用于广泛的平衡约束优化问题。密集高斯-牛顿求解器已经显示出对逆问题有希望的收敛速度，但迄今为止，组装和分解相关矩阵的成本一直是主要的绊脚石。在这项工作中，我们展示了如何将密集的 Gauss-Newton Hessian 矩阵转换为等效的稀疏矩阵，该矩阵可以更有效地进行组装和分解。这导致许多逆问题的计算时间大大减少，我们在一组不同的例子中证明了这一点。