{"ID":2921887,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-03T22:46:55.310989306Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01487","arxiv_id":"2606.01487","title":"Global Convergence of a Line-Search Filter Differential Dynamic Programming Method","abstract":"In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in addition to the dynamics. FilterDDP adopts a line-search filter procedure for step acceptance. However, instead of a damped Newton step applied in the general nonlinear programming setting, the computation of a trial point involves applying a backward recursion and a forward simulation. We establish the global convergence of FilterDDP by showing that for a subset of constrained optimal control problems, the this backward-forward procedure satisfies the same properties as a Newton step for the purpose of establishing global convergence of a line-search filter method, following the analysis of Wächter and Biegler [\\emph{SIAM Journal on Optimization}, 16 (2005), pp. 1-31].","short_abstract":"In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in...","url_abs":"https://arxiv.org/abs/2606.01487","url_pdf":"https://arxiv.org/pdf/2606.01487v1","authors":"[\"Ming Xu\",\"Iman Shames\"]","published":"2026-05-31T23:03:24Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.RO\",\"eess.SY\"]","methods":"[]","has_code":false}