{"paper":{"title":"Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Continuous-time nonlinear programs have asymptotic KKT conditions satisfied along a convergent sequence of approximate solutions.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mois\\'es R. C. do Monte, Rodrigo B. Moreira, Valeriano A. de Oliveira","submitted_at":"2026-05-12T21:02:06Z","abstract_excerpt":"This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of solutions converging to the optimal solution is demonstrated to exist, and such that Karush-Kuhn-Tucker-type conditions are satisfied asymptotically. It is shown that these sequential Karush-Kuhn-Tucker-type conditions also become sufficient for optimality under convexity assumptions. Sequential optimality conditions are a valuable tool for determining when to termi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A sequence of solutions converging to the optimal solution exists such that Karush-Kuhn-Tucker-type conditions are satisfied asymptotically; these conditions are also sufficient under convexity assumptions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The existence of a sequence of approximate solutions that converge to the true optimum while satisfying the asymptotic KKT conditions (implicit in the necessary-conditions claim and not derived from first principles in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The work establishes asymptotic KKT-type necessary optimality conditions for continuous-time nonlinear programming and shows sufficiency under convexity, while proposing a convergent augmented Lagrangian solver.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Continuous-time nonlinear programs have asymptotic KKT conditions satisfied along a convergent sequence of approximate solutions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"40ea8ae4b05ff9d2356e1def4a18c5513dce5facdeaa873da0924d2bc84bbc85"},"source":{"id":"2605.12751","kind":"arxiv","version":1},"verdict":{"id":"6f1a9588-ce66-44de-be2a-025f9c66a19a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:12:05.842932Z","strongest_claim":"A sequence of solutions converging to the optimal solution exists such that Karush-Kuhn-Tucker-type conditions are satisfied asymptotically; these conditions are also sufficient under convexity assumptions.","one_line_summary":"The work establishes asymptotic KKT-type necessary optimality conditions for continuous-time nonlinear programming and shows sufficiency under convexity, while proposing a convergent augmented Lagrangian solver.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The existence of a sequence of approximate solutions that converge to the true optimum while satisfying the asymptotic KKT conditions (implicit in the necessary-conditions claim and not derived from first principles in the abstract).","pith_extraction_headline":"Continuous-time nonlinear programs have asymptotic KKT conditions satisfied along a convergent sequence of approximate solutions."},"references":{"count":40,"sample":[{"doi":"","year":2019,"title":"R. Andreani, N. S. Fazzio, M. L. Schuverdt, and L. D. Secchin. A sequen- tial optimality condition related to the quasi-normality constraint qualifi- cation and its algorithmic consequences.SIAM Journ","work_id":"3bf1c480-66eb-43ea-8895-91adcdd79b6f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"R. Andreani, W. G´ omez, G. Haeser, L. M. Mito, and A. Ramos. On optimality conditions for nonlinear conic programming.Mathematics of Operations Research, 47(3):2160–2185, 2022","work_id":"40eb9ff2-e1cb-4242-876c-b5ac725c4775","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"R. Andreani, P.S. Gon¸ calves, and G. N. Silva. Discrete approximations for strict convex continuous time problems and duality.Comp. Appl. Math., 23:81–105, 2004","work_id":"0284639f-2ff7-4fac-822d-757b267cea62","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"R. Andreani, G. Haeser, and J. M. Mart´ ınez. On sequential optimality conditions for smooth constrained optimization.Optimization, 60(5):627– 641, 2011","work_id":"10f149c4-9563-44e6-a9eb-2a73a97923e8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1902,"title":"R. Andreani, G. Haeser, A. Ramos, and P. J. S. Silva. A second-order se- quential optimality condition associated to the convergence of optimization algorithms.IMA Journal of Numerical Analysis, 37(4)","work_id":"5633b40b-91a8-40b4-84cb-7e6d857295e0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":40,"snapshot_sha256":"a0c706162b9509b2dbad215dc26267b97dd4b23024c10ba78ebe6f9560e5dbe0","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"04a24d6ff27c502d49c32bc7c3ba9d2386d7c29bcc25b4c0d6af071a337426ec"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}