{"paper":{"title":"Global Optimal Trajectory in Chaos and NP-Hardness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"David Yang Gao, Vittorio Latorre","submitted_at":"2015-12-28T08:40:02Z","abstract_excerpt":"This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. The canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by Runge-Kutta type of linear iterations are mainly due to the intrinsic numerical error accumulations. Otherwise, the glo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08343","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}