{"paper":{"title":"Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","math.OC"],"primary_cat":"cs.SY","authors_text":"Choon Yik Tang, Jie Lu","submitted_at":"2011-04-28T15:22:24Z","abstract_excerpt":"This paper presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5422","kind":"arxiv","version":3},"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"}