{"paper":{"title":"Iterative hard-thresholding applied to optimal control problems with $L^0(\\Omega)$ control cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Wachsmuth","submitted_at":"2018-06-01T11:50:31Z","abstract_excerpt":"We investigate the hard-thresholding method applied to optimal control problems with $L^0(\\Omega)$ control cost, which penalizes the measure of the support of the control. As the underlying measure space is non-atomic, arguments of convergence proofs in $l^2$ or $\\mathbb R^n$ cannot be applied. Nevertheless, we prove the surprising property that the values of the objective functional are lower semicontinuous along the iterates. That is, the function value in a weak limit point is less or equal than the lim-inf of the function values along the iterates. Under a compactness assumption, we can pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00297","kind":"arxiv","version":2},"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"}