{"paper":{"title":"Proximal Distance Algorithms: Theory and Examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hua Zhou, Kenneth Lange, Kevin L. Keys","submitted_at":"2016-04-19T19:05:28Z","abstract_excerpt":"Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss $f(\\boldsymbol{x})+\\frac{\\rho}{2}\\mathop{dist}(x,C)^2$ and following the solution $\\boldsymbol{x}_{\\rho}$ to its limit as $\\rho$ tends to $\\infty$. At each iteration the squared Euclidean distance $\\mathop{dist}(\\boldsymbol{x},C)^2$ is majorized by the spherical quadratic $\\| \\boldsymbol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05694","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"}