{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YNXIOVSDFRNOBKMQDEI7XXGEVL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9f4a6978ef5cf04af8ae7a47f9e7ab519a7ee34275783c9ea531f62abbfc9d78","cross_cats_sorted":["math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-29T19:40:25Z","title_canon_sha256":"c7dc063fbc6af8396a12cf4cf44c935fac641bb1871695bcc04233c95e1774ec"},"schema_version":"1.0","source":{"id":"1611.09805","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09805","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09805v4","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09805","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"YNXIOVSDFRNO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YNXIOVSDFRNOBKMQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YNXIOVSD","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:e1cb77fd926ae06febbe7ad5fdcc98dca3ad262429620976df6d5d6c5014fb6c","target":"graph","created_at":"2026-05-18T00:25:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we propose a new primal-dual algorithm for minimizing $f(x) + g(x) + h(Ax)$, where $f$, $g$, and $h$ are proper lower semi-continuous convex functions, $f$ is differentiable with a Lipschitz continuous gradient, and $A$ is a bounded linear operator. The proposed algorithm has some famous primal-dual algorithms for minimizing the sum of two functions as special cases. E.g., it reduces to the Chambolle-Pock algorithm when $f = 0$ and the proximal alternating predictor-corrector when $g = 0$. For the general convex case, we prove the convergence of this new algorithm in terms of th","authors_text":"Ming Yan","cross_cats":["math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-29T19:40:25Z","title":"A new primal-dual algorithm for minimizing the sum of three functions with a linear operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09805","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d05fe65d9f3134dfc67094cd22b5611eafe1cf296404b60388c7b01e5466b7d7","target":"record","created_at":"2026-05-18T00:25:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9f4a6978ef5cf04af8ae7a47f9e7ab519a7ee34275783c9ea531f62abbfc9d78","cross_cats_sorted":["math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-29T19:40:25Z","title_canon_sha256":"c7dc063fbc6af8396a12cf4cf44c935fac641bb1871695bcc04233c95e1774ec"},"schema_version":"1.0","source":{"id":"1611.09805","kind":"arxiv","version":4}},"canonical_sha256":"c36e8756432c5ae0a9901911fbdcc4aaf717c20d84f0f4df888119c30c4d79eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c36e8756432c5ae0a9901911fbdcc4aaf717c20d84f0f4df888119c30c4d79eb","first_computed_at":"2026-05-18T00:25:02.061856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:02.061856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trwgznx1CPpRUNkbfhISZBEAdrrGq0RKKlr/0LcAnesgV8jJ0kB9FM2fWL7nczbB91ZQueFQ3tQGMhIskdT8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:02.062481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09805","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d05fe65d9f3134dfc67094cd22b5611eafe1cf296404b60388c7b01e5466b7d7","sha256:e1cb77fd926ae06febbe7ad5fdcc98dca3ad262429620976df6d5d6c5014fb6c"],"state_sha256":"2f1de9e08f06ca780584751bd59199317cccbfd8afac32b0aaa0dc6c0367a59e"}