{"paper":{"title":"BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Li Zhang, Pengcheng Xie, Wei Hu, Ya-Xiang Yuan","submitted_at":"2026-05-29T04:59:09Z","abstract_excerpt":"Underdetermined quadratic interpolation is a standard model-construction tool in model-based derivative-free trust-region methods: it keeps the number of function evaluations manageable, but leaves many quadratic models consistent with the sampled values. Classical solvers remove this ambiguity by prescribing a norm or a model-change measure, such as the least-Frobenius Hessian update in Powell-type methods. We propose BUP-TR (Bayesian Underdetermined Projection Trust-Region), which replaces this prescribed completion rule by a prior-regularized one. At each iteration, the interpolation equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30841","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/2605.30841/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"}