{"paper":{"title":"Benign Landscape of Quadratic Programs with Orthogonality Constraints and Its Application to Heteroscedastic Probabilistic PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Laura Balzano, Peng Wang, Po Chen, Rujun Jiang","submitted_at":"2026-06-25T15:51:09Z","abstract_excerpt":"In this work, we study the optimization landscape of homogeneous quadratic programs with orthogonality constraints (QPOC) and apply the resulting theory to heteroscedastic probabilistic PCA (HePPCA). For QPOC, we establish a complete characterization of the benign optimization landscape by showing that every critical point is either a global maximizer or a strict saddle point. Our analysis builds on a closed-form characterization of the critical point set, from which we derive a necessary and sufficient condition for global optimality and show that every non-optimal critical point has a direct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27189","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27189/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}