{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QTALH3VHT2XTCKEJLI77F2KDAW","short_pith_number":"pith:QTALH3VH","canonical_record":{"source":{"id":"1606.06219","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-20T17:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"cabecfef3c35841146834c5f3e27ee52e3a5b02050a1e4ef582382a9c81c491e","abstract_canon_sha256":"cc03a7db9dea1006edb0e10b872526e63b41db8d0b12c2749be786c9352e69ac"},"schema_version":"1.0"},"canonical_sha256":"84c0b3eea79eaf3128895a3ff2e943059483da08cfc7168afdf6216ada44ac61","source":{"kind":"arxiv","id":"1606.06219","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06219","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06219v3","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06219","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"QTALH3VHT2XT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QTALH3VHT2XTCKEJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QTALH3VH","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QTALH3VHT2XTCKEJLI77F2KDAW","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06219","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-20T17:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"cabecfef3c35841146834c5f3e27ee52e3a5b02050a1e4ef582382a9c81c491e","abstract_canon_sha256":"cc03a7db9dea1006edb0e10b872526e63b41db8d0b12c2749be786c9352e69ac"},"schema_version":"1.0"},"canonical_sha256":"84c0b3eea79eaf3128895a3ff2e943059483da08cfc7168afdf6216ada44ac61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:41.294634Z","signature_b64":"UzEOJYmx4ctQqXwf3dpz9FuKfhDc9cA7aBht6dMFVA/4fZR6jhA9k0R1wwAePinipTCe2q+1HBtfu3fSUupjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84c0b3eea79eaf3128895a3ff2e943059483da08cfc7168afdf6216ada44ac61","last_reissued_at":"2026-05-18T00:40:41.293769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:41.293769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06219","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TL254tI22alTWSFMtXGiw9r6HLlEzYdRGOWRALNDiTTnErq3MQv48mz2CZS8oqQMwAmUVroqUQ8+GZbY2KuZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:43:01.680575Z"},"content_sha256":"a77cc69528d89d427ea84585377211e7b67b694b77c675aef8d463251d5b7410","schema_version":"1.0","event_id":"sha256:a77cc69528d89d427ea84585377211e7b67b694b77c675aef8d463251d5b7410"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QTALH3VHT2XTCKEJLI77F2KDAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christian Clason, Tuomo Valkonen","submitted_at":"2016-06-20T17:39:16Z","abstract_excerpt":"We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant provided one part of the functional is strongly convex.\n  We show the applicability of the accelerated algorithm to examples of inverse problems with $L^1$- and $L^\\infty$-fitting terms as well as of state-constrained optimal control probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06219","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4L1RP/vRb0+N1aEieKbpEYZ+f9nKoR8J3gWdiRAc3spQKoEtW2/8ZtoTt4tP6B8X4ozutkmYIoK4ABqbmUn/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:43:01.681207Z"},"content_sha256":"fe42e40b70e60ba00b939b20c00f0fc74a47970c6c6dc4c67cff98d9f731d95a","schema_version":"1.0","event_id":"sha256:fe42e40b70e60ba00b939b20c00f0fc74a47970c6c6dc4c67cff98d9f731d95a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTALH3VHT2XTCKEJLI77F2KDAW/bundle.json","state_url":"https://pith.science/pith/QTALH3VHT2XTCKEJLI77F2KDAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTALH3VHT2XTCKEJLI77F2KDAW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T02:43:01Z","links":{"resolver":"https://pith.science/pith/QTALH3VHT2XTCKEJLI77F2KDAW","bundle":"https://pith.science/pith/QTALH3VHT2XTCKEJLI77F2KDAW/bundle.json","state":"https://pith.science/pith/QTALH3VHT2XTCKEJLI77F2KDAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTALH3VHT2XTCKEJLI77F2KDAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QTALH3VHT2XTCKEJLI77F2KDAW","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":"cc03a7db9dea1006edb0e10b872526e63b41db8d0b12c2749be786c9352e69ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-20T17:39:16Z","title_canon_sha256":"cabecfef3c35841146834c5f3e27ee52e3a5b02050a1e4ef582382a9c81c491e"},"schema_version":"1.0","source":{"id":"1606.06219","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06219","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06219v3","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06219","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"QTALH3VHT2XT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QTALH3VHT2XTCKEJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QTALH3VH","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:fe42e40b70e60ba00b939b20c00f0fc74a47970c6c6dc4c67cff98d9f731d95a","target":"graph","created_at":"2026-05-18T00:40:41Z","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":"We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant provided one part of the functional is strongly convex.\n  We show the applicability of the accelerated algorithm to examples of inverse problems with $L^1$- and $L^\\infty$-fitting terms as well as of state-constrained optimal control probl","authors_text":"Christian Clason, Tuomo Valkonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-20T17:39:16Z","title":"Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06219","kind":"arxiv","version":3},"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:a77cc69528d89d427ea84585377211e7b67b694b77c675aef8d463251d5b7410","target":"record","created_at":"2026-05-18T00:40:41Z","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":"cc03a7db9dea1006edb0e10b872526e63b41db8d0b12c2749be786c9352e69ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-20T17:39:16Z","title_canon_sha256":"cabecfef3c35841146834c5f3e27ee52e3a5b02050a1e4ef582382a9c81c491e"},"schema_version":"1.0","source":{"id":"1606.06219","kind":"arxiv","version":3}},"canonical_sha256":"84c0b3eea79eaf3128895a3ff2e943059483da08cfc7168afdf6216ada44ac61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84c0b3eea79eaf3128895a3ff2e943059483da08cfc7168afdf6216ada44ac61","first_computed_at":"2026-05-18T00:40:41.293769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:41.293769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzEOJYmx4ctQqXwf3dpz9FuKfhDc9cA7aBht6dMFVA/4fZR6jhA9k0R1wwAePinipTCe2q+1HBtfu3fSUupjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:41.294634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06219","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a77cc69528d89d427ea84585377211e7b67b694b77c675aef8d463251d5b7410","sha256:fe42e40b70e60ba00b939b20c00f0fc74a47970c6c6dc4c67cff98d9f731d95a"],"state_sha256":"6bb214e6e4596dea8b2118a85cdf0ad5d145dde2040d409c17b87d949dcaef0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVC2sLG4e2oPa0VWiJKonJF3PvXDEdlOapxm9K6m8dp1FXJavmd1hh5NZpyQNLVcjQqxxQOLSXG2D7Lzzc6WDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:43:01.684396Z","bundle_sha256":"218813081ef6a6a4516b7c988c73083e24380abdcdc97fe89bd7b97eeaa83c36"}}