{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EGYY4SRHKJOFC3ACMOZDIVLMP2","short_pith_number":"pith:EGYY4SRH","schema_version":"1.0","canonical_sha256":"21b18e4a27525c516c0263b234556c7e8fcec26856d1b4af77208014c89b90be","source":{"kind":"arxiv","id":"1804.10243","version":4},"attestation_state":"computed","paper":{"title":"Sparse Inverse Problems Over Measures: Equivalence of the Conditional Gradient and Exchange Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrew Thompson, Armin Eftekhari","submitted_at":"2018-04-26T18:51:05Z","abstract_excerpt":"We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a `continuum-of-subspaces' model, a recent trend with applications in signal processing, machine learning, and high-dimensional statistics. We prove that the conditional gradient method (CGM) applied to this infinite-dimensional program, as proposed recently in the literature, is equivalent to the exchange method (EM) applied to its Lagrangian dual, which is a semi-infinite progr"},"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":"1804.10243","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-26T18:51:05Z","cross_cats_sorted":[],"title_canon_sha256":"57637c53e26acf112642bdca149c3e613a0ad9bbed64395a51a9a3c088a70091","abstract_canon_sha256":"6029bc514a3ba05b5e9510d5b884dd2b2b34963cf6dde68257e4e63114ad9df0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:07.753605Z","signature_b64":"ZkkE0xHezFAeBM9DYS7kiQL90JH3FmAoWKhaf7IcBATKncbwVBkffsFa01AOnPMhaGLAK9jfeARupcqNp7klDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21b18e4a27525c516c0263b234556c7e8fcec26856d1b4af77208014c89b90be","last_reissued_at":"2026-05-17T23:52:07.753211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:07.753211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse Inverse Problems Over Measures: Equivalence of the Conditional Gradient and Exchange Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrew Thompson, Armin Eftekhari","submitted_at":"2018-04-26T18:51:05Z","abstract_excerpt":"We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a `continuum-of-subspaces' model, a recent trend with applications in signal processing, machine learning, and high-dimensional statistics. We prove that the conditional gradient method (CGM) applied to this infinite-dimensional program, as proposed recently in the literature, is equivalent to the exchange method (EM) applied to its Lagrangian dual, which is a semi-infinite progr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10243","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.10243","created_at":"2026-05-17T23:52:07.753277+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.10243v4","created_at":"2026-05-17T23:52:07.753277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10243","created_at":"2026-05-17T23:52:07.753277+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGYY4SRHKJOF","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGYY4SRHKJOFC3AC","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGYY4SRH","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09919","citing_title":"On the linear convergence rates of exchange and continuous methods for total variation minimization","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2","json":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2.json","graph_json":"https://pith.science/api/pith-number/EGYY4SRHKJOFC3ACMOZDIVLMP2/graph.json","events_json":"https://pith.science/api/pith-number/EGYY4SRHKJOFC3ACMOZDIVLMP2/events.json","paper":"https://pith.science/paper/EGYY4SRH"},"agent_actions":{"view_html":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2","download_json":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2.json","view_paper":"https://pith.science/paper/EGYY4SRH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.10243&json=true","fetch_graph":"https://pith.science/api/pith-number/EGYY4SRHKJOFC3ACMOZDIVLMP2/graph.json","fetch_events":"https://pith.science/api/pith-number/EGYY4SRHKJOFC3ACMOZDIVLMP2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2/action/storage_attestation","attest_author":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2/action/author_attestation","sign_citation":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2/action/citation_signature","submit_replication":"https://pith.science/pith/EGYY4SRHKJOFC3ACMOZDIVLMP2/action/replication_record"}},"created_at":"2026-05-17T23:52:07.753277+00:00","updated_at":"2026-05-17T23:52:07.753277+00:00"}