{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OPJFQWZZBHH7TMB34CPUKTPBXN","short_pith_number":"pith:OPJFQWZZ","schema_version":"1.0","canonical_sha256":"73d2585b3909cff9b03be09f454de1bb50619046039309b50fc565f4a3d77729","source":{"kind":"arxiv","id":"1504.05002","version":1},"attestation_state":"computed","paper":{"title":"Linearly Convergent Away-Step Conditional Gradient for Non-strongly Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Amir Beck, Shimrit Shtern","submitted_at":"2015-04-20T10:32:50Z","abstract_excerpt":"We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that the conditional gradient method with away steps employed on the aforementioned problem without the additional linear term has linear rate of convergence, depending on the so-called pyramidal width of the feasible set. We revisit this result and provide a variant of the algorithm and an analysis that is based on simple duality arguments, as well as correspondi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.05002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-20T10:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"00c471d5fb3ac4859cc751e6ae646baec84ab0dfb5db4940002bc6b663216a6c","abstract_canon_sha256":"bf045adda3bf0fc6cefa7b66a90acce987fe8af2ac6b2747c3fd363b5d530860"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:22.975089Z","signature_b64":"TGFIUxPHzmMZX3E3I0ucg6swj73irqdjo54UdstPCk0+SXRkv0nSA8rN1nzsA0JBOIrC94YL4j+C1T48NVDTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73d2585b3909cff9b03be09f454de1bb50619046039309b50fc565f4a3d77729","last_reissued_at":"2026-05-18T02:18:22.974350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:22.974350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linearly Convergent Away-Step Conditional Gradient for Non-strongly Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Amir Beck, Shimrit Shtern","submitted_at":"2015-04-20T10:32:50Z","abstract_excerpt":"We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that the conditional gradient method with away steps employed on the aforementioned problem without the additional linear term has linear rate of convergence, depending on the so-called pyramidal width of the feasible set. We revisit this result and provide a variant of the algorithm and an analysis that is based on simple duality arguments, as well as correspondi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05002","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.05002","created_at":"2026-05-18T02:18:22.974468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05002v1","created_at":"2026-05-18T02:18:22.974468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05002","created_at":"2026-05-18T02:18:22.974468+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPJFQWZZBHH7","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPJFQWZZBHH7TMB3","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPJFQWZZ","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN","json":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN.json","graph_json":"https://pith.science/api/pith-number/OPJFQWZZBHH7TMB34CPUKTPBXN/graph.json","events_json":"https://pith.science/api/pith-number/OPJFQWZZBHH7TMB34CPUKTPBXN/events.json","paper":"https://pith.science/paper/OPJFQWZZ"},"agent_actions":{"view_html":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN","download_json":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN.json","view_paper":"https://pith.science/paper/OPJFQWZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05002&json=true","fetch_graph":"https://pith.science/api/pith-number/OPJFQWZZBHH7TMB34CPUKTPBXN/graph.json","fetch_events":"https://pith.science/api/pith-number/OPJFQWZZBHH7TMB34CPUKTPBXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN/action/storage_attestation","attest_author":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN/action/author_attestation","sign_citation":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN/action/citation_signature","submit_replication":"https://pith.science/pith/OPJFQWZZBHH7TMB34CPUKTPBXN/action/replication_record"}},"created_at":"2026-05-18T02:18:22.974468+00:00","updated_at":"2026-05-18T02:18:22.974468+00:00"}