Faster reconstruction algorithms with stronger convergence guarantees

Develop faster algorithms with stronger convergence guarantees for the nonlinear least-squares reconstruction of vertex wave speeds from time-dependent graph-wave measurements.

Background

The paper reconstructs vertex wave speeds by minimizing a bounded nonlinear least-squares objective whose residuals are generated by solving the graph wave equation and its sensitivity equations. The authors prove convergence of global minimizers of the temporally discretized objective to the unique continuous-time minimizer under their identifiability assumptions.

However, the implemented trust-region reflective method is local, and the objective is generally nonconvex. Consequently, the paper does not provide a computational method that is both faster and equipped with stronger guarantees concerning convergence of the optimization iterates. The authors explicitly leave development of such methods for future work.