{"paper":{"title":"More Virtuous Smoothing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daphne Skipper, Jon Lee, Luze Xu","submitted_at":"2018-02-26T00:30:45Z","abstract_excerpt":"In the context of global optimization of mixed-integer nonlinear optimization formulations, we consider smoothing univariate functions $f$ that satisfy $f(0)=0$, $f$ is increasing and concave on $[0,+\\infty)$, $f$ is twice differentiable on all of $(0,+\\infty)$, but $f'(0)$ is undefined or intolerably large. The canonical examples are root functions $f(w):=w^p$, for $0<p<1$. We consider the earlier approach of defining a smoothing function $g$ that is identical with $f$ on $(\\delta,+\\infty)$, for some chosen $\\delta>0$, then replacing the part of $f$ on $[0,\\delta]$ with the unique homogeneous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09112","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"}