Convergence theory and basin characterization for nonlinear spectral recovery

Establish convergence guarantees for majorization-minimization or successive-convex-approximation methods applied to the rational exact-model fixed-point criterion, or characterize the criterion’s basins of attraction, to provide a reliable computational method for nonlinear spectral recovery.

Background

The exact nonlinear least-squares formulation is theoretically identified but empirically nonconvex: initialization at the truth performs well, whereas initialization at first-order estimates can converge to spectral-inflating ridges. Profiling out the nuisance confound does not resolve this geometry.

The paper proposes majorization-minimization and successive-convex-approximation procedures as natural globalization devices, but leaves their convergence behavior and the structure of the objective’s attraction basins unresolved. These results are needed for a usable exact-model alternative to the heuristic two-stage inversion.

References

The Jacobian already derived for Theorem~\ref{thm:nonlinear} supports Gauss--Newton and Levenberg--Marquardt steps on the reduced problem, and majorization-minimization or successive-convex-approximation surrogates are the natural globalization devices; their convergence theory for this rational fixed-point criterion, or a characterization of its basins, is therefore the computational half of the open spectral-inference problem, alongside the statistical half above.

— Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation  (2608.25844 - Woo, 26 Aug 2026) in Section 5, subsection “Uncertainty quantification for spectral alarms”