{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XZPY2YGEVML35VEVN4Q65JSOQ3","short_pith_number":"pith:XZPY2YGE","schema_version":"1.0","canonical_sha256":"be5f8d60c4ab17bed4956f21eea64e86e058544a4902337bc272e63933e74459","source":{"kind":"arxiv","id":"1703.10637","version":1},"attestation_state":"computed","paper":{"title":"Convergence of a Scholtes-type Regularization Method for Cardinality-Constrained Optimization Problems with an Application in Sparse Robust Portfolio Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexandra Schwartz, Martin Branda, Max Bucher, Michal \\v{C}ervinka","submitted_at":"2017-03-30T18:49:26Z","abstract_excerpt":"We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming problem, which is thus still difficult to solve. Therefore, we apply a Scholtes-type regularization method to obtain a sequence of easier to solve problems and investigate the convergence of the obtained KKT points. We show that such a sequence converges to an S-stationary point, which corresponds to a local minimizer of the original problem under the assumption o"},"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":"1703.10637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-30T18:49:26Z","cross_cats_sorted":[],"title_canon_sha256":"c3a6113408122efd83ad73487111685ce497921a112f39e753f965684b3ce9fa","abstract_canon_sha256":"003342b3038f39fdbd2d06d25c0989b84de4914acec64e7e60b6040d49a0ef09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:33.104812Z","signature_b64":"Z75G4vDy0POZl8HVEzs/uSfwsAOu816EjorWRVL7dtQym8HYicdmhVd9l7k3rAWduKEkJRz4XjCWX2VULUM6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be5f8d60c4ab17bed4956f21eea64e86e058544a4902337bc272e63933e74459","last_reissued_at":"2026-05-18T00:47:33.104279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:33.104279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of a Scholtes-type Regularization Method for Cardinality-Constrained Optimization Problems with an Application in Sparse Robust Portfolio Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexandra Schwartz, Martin Branda, Max Bucher, Michal \\v{C}ervinka","submitted_at":"2017-03-30T18:49:26Z","abstract_excerpt":"We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming problem, which is thus still difficult to solve. Therefore, we apply a Scholtes-type regularization method to obtain a sequence of easier to solve problems and investigate the convergence of the obtained KKT points. We show that such a sequence converges to an S-stationary point, which corresponds to a local minimizer of the original problem under the assumption o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10637","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":"1703.10637","created_at":"2026-05-18T00:47:33.104388+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10637v1","created_at":"2026-05-18T00:47:33.104388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10637","created_at":"2026-05-18T00:47:33.104388+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZPY2YGEVML3","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZPY2YGEVML35VEV","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZPY2YGE","created_at":"2026-05-18T12:31:56.362134+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/XZPY2YGEVML35VEVN4Q65JSOQ3","json":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3.json","graph_json":"https://pith.science/api/pith-number/XZPY2YGEVML35VEVN4Q65JSOQ3/graph.json","events_json":"https://pith.science/api/pith-number/XZPY2YGEVML35VEVN4Q65JSOQ3/events.json","paper":"https://pith.science/paper/XZPY2YGE"},"agent_actions":{"view_html":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3","download_json":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3.json","view_paper":"https://pith.science/paper/XZPY2YGE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10637&json=true","fetch_graph":"https://pith.science/api/pith-number/XZPY2YGEVML35VEVN4Q65JSOQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/XZPY2YGEVML35VEVN4Q65JSOQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3/action/storage_attestation","attest_author":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3/action/author_attestation","sign_citation":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3/action/citation_signature","submit_replication":"https://pith.science/pith/XZPY2YGEVML35VEVN4Q65JSOQ3/action/replication_record"}},"created_at":"2026-05-18T00:47:33.104388+00:00","updated_at":"2026-05-18T00:47:33.104388+00:00"}