{"paper":{"title":"Variational Analysis for the Bilateral Minimal Time Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Luong V. Nguyen","submitted_at":"2017-05-09T09:40:09Z","abstract_excerpt":"In this paper, we derive formulas for the Fr\\'echet (singular) subdiferentials of the bilateral minimal time function $T:\\mathbb{R}^n \\times \\mathbb{R}^n \\to [0,+\\infty]$ associated with a system governed by differential inclusions. As a consequence, we give a connection between the Fr\\'echet normals to the sub-level sets of $T$ and to its epigraph. Finally, we show that the Fr\\'echet normal cones to the sub-level set of $T$ at a point $(\\alpha,\\beta)$ and to epi($T$) at $((\\alpha,\\beta),T(\\alpha,\\beta))$ have the same dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03249","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"}