{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U6RMNFEFQYAMLNHJEL7ZYWWDL7","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":"5e20b57b1c06e8f7eefed59f4a09b91058072672ef7b170ce384e0752894ee15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-04T08:28:30Z","title_canon_sha256":"d8b7b2508cebb7a6be138ac7c5c4911794f53ef7b9e6227305a5289e11349116"},"schema_version":"1.0","source":{"id":"1805.01656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01656","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01656v1","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01656","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"pith_short_12","alias_value":"U6RMNFEFQYAM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U6RMNFEFQYAMLNHJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U6RMNFEF","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:be30f6b8d159befa613fcb1b8c243d1ec051410003a5aea88d973788f846694d","target":"graph","created_at":"2026-05-18T00:16:47Z","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":"As a complement to two recent papers by An and Yen [An, D.T.V., Yen, N.D.: Differential stability of convex optimization problems under inclusion constraints. Appl. Anal., 94, 108--128 (2015)], and by An and Yao [An, D.T.V., Yao, J.-C.: Further results on differential stability of convex optimization problems. J. Optim. Theory Appl., 170, 28--42 (2016)] on subdifferentials of the optimal value function of infinite-dimensional convex optimization problems, this paper studies the differential stability of convex optimization problems, where the solution set may be empty. By using a suitable sum ","authors_text":"Duong Thi Viet An, Jen-Chih Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-04T08:28:30Z","title":"Differential stability of convex optimization problems with possibly empty solution sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01656","kind":"arxiv","version":1},"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:bd5afec0299bc6edff62e301a62df62ae6a2787e0541d33d76c0cb2a73c27f43","target":"record","created_at":"2026-05-18T00:16:47Z","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":"5e20b57b1c06e8f7eefed59f4a09b91058072672ef7b170ce384e0752894ee15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-04T08:28:30Z","title_canon_sha256":"d8b7b2508cebb7a6be138ac7c5c4911794f53ef7b9e6227305a5289e11349116"},"schema_version":"1.0","source":{"id":"1805.01656","kind":"arxiv","version":1}},"canonical_sha256":"a7a2c694858600c5b4e922ff9c5ac35fc6ab901006e9553828f7ceb188ce3da1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7a2c694858600c5b4e922ff9c5ac35fc6ab901006e9553828f7ceb188ce3da1","first_computed_at":"2026-05-18T00:16:47.166476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:47.166476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MMQH5yN346aVvBEPesQccCO5gF9ojxKZJ16e2yhsomNp+uGrXGlZTFzyQnbbkkAex/QWdE7kYSrJSTSl7A3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:47.167281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd5afec0299bc6edff62e301a62df62ae6a2787e0541d33d76c0cb2a73c27f43","sha256:be30f6b8d159befa613fcb1b8c243d1ec051410003a5aea88d973788f846694d"],"state_sha256":"c73074d003645677a28a6ef0b74b0ef15d68763402f119721678af66df7a368f"}