{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3AFZV76FGWEMAMBB3TS2ERYYBO","short_pith_number":"pith:3AFZV76F","canonical_record":{"source":{"id":"1104.5351","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-28T10:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"b921a0d471c487191d90d223dfca515c3660b5de845b6542fd4893cc44711447","abstract_canon_sha256":"ea4b2ac8f0516be94b4a5ada28384623d254bd776bd52f79cbfcffaecb8d2d25"},"schema_version":"1.0"},"canonical_sha256":"d80b9affc53588c03021dce5a247180b9e6f08af4f2cd9be0a7472dfdac54adf","source":{"kind":"arxiv","id":"1104.5351","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5351","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5351v4","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5351","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"3AFZV76FGWEM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3AFZV76FGWEMAMBB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3AFZV76F","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3AFZV76FGWEMAMBB3TS2ERYYBO","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5351","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-28T10:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"b921a0d471c487191d90d223dfca515c3660b5de845b6542fd4893cc44711447","abstract_canon_sha256":"ea4b2ac8f0516be94b4a5ada28384623d254bd776bd52f79cbfcffaecb8d2d25"},"schema_version":"1.0"},"canonical_sha256":"d80b9affc53588c03021dce5a247180b9e6f08af4f2cd9be0a7472dfdac54adf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:00.807197Z","signature_b64":"JbPYq5skN+d7YmuEX2YrmcHTppniXeOAANtrYsSmiHJsvbzqlsnd3S/MxXxtjOG5s0yp4yp3I9sXteiuhL3OBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80b9affc53588c03021dce5a247180b9e6f08af4f2cd9be0a7472dfdac54adf","last_reissued_at":"2026-05-18T02:22:00.806535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:00.806535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5351","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOPUo4Fsqh4hh6tVLZX3z52aa/V5DbzWB8uGAh/H/j+7gFJ7M1RbEdc2ByqMDkp+mQ07qGiVtA3rN3dvM2YSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:05:27.373385Z"},"content_sha256":"1f64881e0d2cc02cda9faaf03b03dffc199901bf9623ede89ddf9cba64245a0b","schema_version":"1.0","event_id":"sha256:1f64881e0d2cc02cda9faaf03b03dffc199901bf9623ede89ddf9cba64245a0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3AFZV76FGWEMAMBB3TS2ERYYBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas M. Tillmann, Dirk A. Lorenz, Marc E. Pfetsch","submitted_at":"2011-04-28T10:37:55Z","abstract_excerpt":"We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Nevertheless, we provide conditions which ensure convergence to an optimal feasible point under suitable assumptions. One convergence result deals with step size sequences that are fixed a priori. Two other result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5351","kind":"arxiv","version":4},"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":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOWC+kOKTBOSxY6W5XTS+bCCgPfqLDH+A3AsP17sqjguxCGJ5u59IS7owWujy8uFRg/pJMUYd/z3AAzt8ZiNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T15:05:27.373734Z"},"content_sha256":"ac1f8415c5d5138f756d084830fbb2c09bb36426534033f00e36d997069fe9c9","schema_version":"1.0","event_id":"sha256:ac1f8415c5d5138f756d084830fbb2c09bb36426534033f00e36d997069fe9c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/bundle.json","state_url":"https://pith.science/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/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":"2026-05-20T15:05:27Z","links":{"resolver":"https://pith.science/pith/3AFZV76FGWEMAMBB3TS2ERYYBO","bundle":"https://pith.science/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/bundle.json","state":"https://pith.science/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AFZV76FGWEMAMBB3TS2ERYYBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3AFZV76FGWEMAMBB3TS2ERYYBO","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":"ea4b2ac8f0516be94b4a5ada28384623d254bd776bd52f79cbfcffaecb8d2d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-28T10:37:55Z","title_canon_sha256":"b921a0d471c487191d90d223dfca515c3660b5de845b6542fd4893cc44711447"},"schema_version":"1.0","source":{"id":"1104.5351","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5351","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5351v4","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5351","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"3AFZV76FGWEM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3AFZV76FGWEMAMBB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3AFZV76F","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ac1f8415c5d5138f756d084830fbb2c09bb36426534033f00e36d997069fe9c9","target":"graph","created_at":"2026-05-18T02:22:00Z","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 propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Nevertheless, we provide conditions which ensure convergence to an optimal feasible point under suitable assumptions. One convergence result deals with step size sequences that are fixed a priori. Two other result","authors_text":"Andreas M. Tillmann, Dirk A. Lorenz, Marc E. Pfetsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-28T10:37:55Z","title":"An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5351","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":"sha256:1f64881e0d2cc02cda9faaf03b03dffc199901bf9623ede89ddf9cba64245a0b","target":"record","created_at":"2026-05-18T02:22:00Z","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":"ea4b2ac8f0516be94b4a5ada28384623d254bd776bd52f79cbfcffaecb8d2d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-28T10:37:55Z","title_canon_sha256":"b921a0d471c487191d90d223dfca515c3660b5de845b6542fd4893cc44711447"},"schema_version":"1.0","source":{"id":"1104.5351","kind":"arxiv","version":4}},"canonical_sha256":"d80b9affc53588c03021dce5a247180b9e6f08af4f2cd9be0a7472dfdac54adf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d80b9affc53588c03021dce5a247180b9e6f08af4f2cd9be0a7472dfdac54adf","first_computed_at":"2026-05-18T02:22:00.806535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:00.806535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JbPYq5skN+d7YmuEX2YrmcHTppniXeOAANtrYsSmiHJsvbzqlsnd3S/MxXxtjOG5s0yp4yp3I9sXteiuhL3OBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:00.807197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5351","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f64881e0d2cc02cda9faaf03b03dffc199901bf9623ede89ddf9cba64245a0b","sha256:ac1f8415c5d5138f756d084830fbb2c09bb36426534033f00e36d997069fe9c9"],"state_sha256":"b7b0104db47a8515b9a71417257e34427bd6d8f98a9ab78853bd11973df8ef2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i7MEbvv5V2OnVzj07mXvYBk35LbyyIPPyan+aUtM8/IKJf3UMPe/NDPDz3EpDEpaXjRjZPZ6MDDb2NVwwE0XDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T15:05:27.376159Z","bundle_sha256":"67f74ec6958003637e240a9922b353c3f1e28c9a1ed27a7f8a1d8f9250c1defd"}}