{"paper":{"title":"Double Well Potential Function and Its Optimization in the n-dimensional Real Space - Part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing, Yong Xia","submitted_at":"2014-04-07T22:27:59Z","abstract_excerpt":"In contrast to taking the dual approach for finding a global minimum solution of a double well potential function, in Part II of the paper, we characterize a local minimizer, local maximizer, and global minimizer directly from the primal side. It is proven that, for a ``nonsingular\" double well function, there exists at most one local, but non-global, minimizer and at most one local maximizer. Moreover, when it exists, the local maximizer is ``surrounded\" by local minimizers in the sense that the norm of the local maximizer is strictly less than that of any local minimizer. We also establish s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1963","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"}