Cyclic seesaw optimization and identification

In the seesaw (or cyclic or alternating) method for optimization and identification, the full parameter vector is divided into two or more subvectors and the process proceeds by sequentially optimizing each of the subvectors while holding the remaining parameters at their most recent values. One advantage of the scheme is the preservation of large investments in software while allowing for an extension of capability to include new parameters for estimation. A specific case involves cross-sectional data represented in state-space form, where there is interest in estimating the mean vector and covariance matrix of the initial state vector as well as parameters associated with the dynamics of the underlying differential equations. This paper shows that under reasonable conditions the cyclic scheme leads to parameter estimates that converge to the optimal joint value for the full vector of unknown parameters. Convergence conditions here differ from others in the literature. Further, relative to standard search methods on the full vector, numerical results here suggest a more general property of faster convergence as a consequence of the more “aggressive” (larger) gain coefficient (step size) possible in the seesaw algorithm.