{"paper":{"title":"Computing exact $D$-optimal designs by mixed integer second-order cone programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Guillaume Sagnol, Radoslav Harman","submitted_at":"2013-07-18T14:16:16Z","abstract_excerpt":"Let the design of an experiment be represented by an $s$-dimensional vector $\\mathbf {w}$ of weights with nonnegative components. Let the quality of $\\mathbf {w}$ for the estimation of the parameters of the statistical model be measured by the criterion of $D$-optimality, defined as the $m$th root of the determinant of the information matrix $M(\\mathbf {w})=\\sum_{i=1}^sw_iA_iA_i^T$, where $A_i,i=1,\\ldots,s$ are known matrices with $m$ rows. In this paper, we show that the criterion of $D$-optimality is second-order cone representable. As a result, the method of second-order cone programming ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4953","kind":"arxiv","version":3},"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"}