{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T00:19:15Z","timestamp":1743121155205,"version":"3.40.3"},"publisher-location":"Cham","reference-count":11,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031105616"},{"type":"electronic","value":"9783031105623"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"vor","delay-in-days":215,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>\nThe concept of exploiting proven monotonicity for dimension reduction and elimination of partition sets is well known in the field of Interval Arithmetic Branch and Bound (B &amp;B). Part of the concepts can be applied in simplicial B &amp;B over a box. The focus of our research is here on minimizing a function over a lower simplicial dimension feasible set, like in blending and portfolio optimization problems. How can monotonicity be detected and be exploited in a B &amp;B context? We found that feasible directions can be used to derive bounds on the directional derivative. Specifically, Linear Programming can be used to detect the sharpest bounds.<\/jats:p>","DOI":"10.1007\/978-3-031-10562-3_9","type":"book-chapter","created":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T14:25:15Z","timestamp":1659536715000},"page":"113-126","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Monotonicity Detection in\u00a0Simplicial Branch and\u00a0Bound over\u00a0a\u00a0Simplex"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8459-4982","authenticated-orcid":false,"given":"L. 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