SGN: Sparse Gauss-Newton for Accelerated Sensitivity Analysis

TL;DR

This paper introduces a sparse Gauss-Newton solver that significantly accelerates sensitivity analysis in equilibrium-constrained optimization problems by transforming dense matrices into sparse ones, reducing computation time.

Contribution

The authors develop a method to convert dense Gauss-Newton Hessians into sparse matrices, enabling more efficient assembly and factorization for inverse problems.

Findings

Drastically reduced computation times demonstrated on diverse examples

Established theoretical links between sensitivity analysis and nonlinear programming

Proved equivalence of methods under specific assumptions

Abstract

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.