  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.
