{"paper":{"title":"Quasi-Leontief utility functions on partially ordered sets I: efficient points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Charles Horvath, QiBin Liang, Walter Briec","submitted_at":"2011-02-14T09:34:39Z","abstract_excerpt":"A function $u: X\\to\\mathbb{R}$ defined on a partially ordered set is quasi-Leontief if, if for all $x\\in X$, the upper level set $\\{x^\\prime\\in X: u(x^\\prime)\\geqslant u(x)\\} $ has a smallest element. A function $u: \\prod_{j=1}^nX_j\\to\\mathbb{R}$ whose partial functions obtained by freezing $n-1$ of the variables are all quasi-Leontief is an individually quasi-Leontief function; a point $x$ of the product space is an efficient point for $u$ if it is a minimal element of $\\{x^\\prime\\in X: u(x^\\prime)\\geqslant u(x)\\} $. Part I deals with the maximisation of quasi-Leontief functions and the exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2710","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"}