{"paper":{"title":"${\\varepsilon}$-optimality in reverse convex optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"H. Sellak, M. El Maghri","submitted_at":"2025-05-31T17:02:29Z","abstract_excerpt":"We characterize approximate global optimal solutions (${\\varepsilon}$-optima) to reverse optimization problems, namely, problems whose non-convex constraint is of the form $h(x) \\geq 0$. This issue has not been addressed previously in the literature. Our idea consists of converting the reverse program into an unconstrained bicriteria DC program. The main condition presented is obtained in terms of Fenchel's ${\\varepsilon}$-subdifferentials thanks to an earlier result in difference vector optimization by El Maghri. This extends and improves similar results from the literature dealing with exact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.00638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}