{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T14:32:33Z","timestamp":1761921153531,"version":"3.37.3"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This study focuses on exhaustive global optimization algorithms over a simplicial feasible set with simplicial partition sets. Bounds on the objective function value and its partial derivative are based on interval automatic differentiation over the interval hull of a simplex. A monotonicity test may be used to decide to either reject a simplicial partition set or to reduce its simplicial dimension to a relative border (at the boundary of the feasible set) facet (or face) by removing one (or more) vertices. A monotonicity test is more complicated for a simplicial sub-set than for a box, because its orientation does not coincide with the components of the gradient. However, one can focus on directional derivatives (DD). In a previous study, we focused on either basic directions, such as centroid to vertex or vertex to vertex directions, or finding the best directional derivative by solving an LP or MIP. The research question of this paper refers to using local search (LS) based sampling of directions from vertex to facet. Results show that most of the monotonic DD found by LP are also found by LS, but with much less computational cost. Notice that finding a monotone direction does not require to find the direction in which a derivative bound is the steepest.\n<\/jats:p>","DOI":"10.1007\/s10898-023-01310-y","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T02:01:26Z","timestamp":1689040886000},"page":"311-330","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Local search versus linear programming to detect monotonicity in simplicial branch and bound"],"prefix":"10.1007","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8459-4982","authenticated-orcid":false,"given":"L. G.","family":"Casado","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0927-111X","authenticated-orcid":false,"given":"B.","family":"G.-T\u00f3th","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1572-1436","authenticated-orcid":false,"given":"E. M. T.","family":"Hendrix","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6457-3321","authenticated-orcid":false,"given":"F.","family":"Messine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"issue":"3","key":"1310_CR1","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1007\/s10898-011-9771-5","volume":"56","author":"JL Berenguel","year":"2013","unstructured":"Berenguel, J.L., Casado, L., Garc\u00eda, I., Hendrix, E.: On estimating workload in interval branch-and-bound global optimization algorithms. J. Global Optim. 56(3), 821\u2013844 (2013). https:\/\/doi.org\/10.1007\/s10898-011-9771-5","journal-title":"J. Global Optim."},{"key":"1310_CR2","doi-asserted-by":"publisher","unstructured":"Casado, L.G., G.-T\u00f3th, B., Hendrix, E.M.T., Messine, F.: On monotonicity detection in simplicial branch and bound over a simplex. In: Computational Science and Its Applications \u2013 ICCSA 2022 Workshops, pp. 113\u2013126. Springer International Publishing, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-10562-3_9","DOI":"10.1007\/978-3-031-10562-3_9"},{"issue":"4","key":"1310_CR3","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/s10898-007-9157-x","volume":"39","author":"LG Casado","year":"2007","unstructured":"Casado, L.G., Hendrix, E.M.T., Garc\u00eda, I.: Infeasibility spheres for finding robust solutions of blending problems with quadratic constraints. J. Global Optim. 39(4), 577\u2013593 (2007). https:\/\/doi.org\/10.1007\/s10898-007-9157-x","journal-title":"J. Global Optim."},{"issue":"3","key":"1310_CR4","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/BF01096455","volume":"5","author":"K Du","year":"1994","unstructured":"Du, K., Kearfott, R.B.: The cluster problem in multivariate global optimization. J. Global Optim. 5(3), 253\u2013265 (1994)","journal-title":"J. Global Optim."},{"issue":"4","key":"1310_CR5","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1007\/s10898-021-01053-8","volume":"80","author":"B G.-T\u00f3th","year":"2021","unstructured":"G.-T\u00f3th, B., Casado, L.G., Hendrix, E.M.T., Messine, F.: On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic. J. Global Optim. 80(4), 779\u2013804 (2021)","journal-title":"J. Global Optim."},{"key":"1310_CR6","doi-asserted-by":"crossref","unstructured":"G.-T\u00f3th, B., Hendrix, E.M.T., Casado, L.G.: On monotonicity and search strategies in face based copositivity detection algorithms. Central Eur. J. Oper. Res. (2021)","DOI":"10.1007\/s10100-021-00737-6"},{"key":"1310_CR7","volume-title":"Global Optimization Using Interval Analysis, 2$$^{nd}$$ edn","author":"E Hansen","year":"2004","unstructured":"Hansen, E., Walster, W.: Global Optimization Using Interval Analysis, 2$$^{nd}$$ edn. Marcel Dekker Inc., New York (2004)"},{"key":"1310_CR8","doi-asserted-by":"publisher","unstructured":"Hendrix, E., Salmer\u00f3n, J., Casado, L.: On function monotonicity in simplicial branch and bound. In: LeGO 2018, p.\u00a04. Leiden (The Netherlands) (2018). https:\/\/doi.org\/10.1063\/1.5089974","DOI":"10.1063\/1.5089974"},{"issue":"218","key":"1310_CR9","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1090\/s0025-5718-97-00809-0","volume":"66","author":"R Horst","year":"1997","unstructured":"Horst, R.: On generalized bisection of $$n$$-simplices. Math. Comput. 66(218), 691\u2013699 (1997). https:\/\/doi.org\/10.1090\/s0025-5718-97-00809-0","journal-title":"Math. Comput."},{"key":"1310_CR10","unstructured":"Karhbet, S.D., Kearfott, R.B.: Range bounds of functions over simplices, for branch and bound algorithms. Reliab. Comput. 25, 53\u201373 (2017). Reliab.-Comput.-J"},{"key":"1310_CR11","doi-asserted-by":"publisher","unstructured":"Kearfott, B., Du, K.: The Cluster Problem in Global Optimization: the Univariate Case, pp. 117\u2013127. Springer, Vienna (1993). https:\/\/doi.org\/10.1007\/978-3-7091-6918-6_10","DOI":"10.1007\/978-3-7091-6918-6_10"},{"key":"1310_CR12","unstructured":"Li, Q., McKenzie, D., Yin, W.: From the simplex to the sphere: faster constrained optimization using the hadamard parametrization (2021). arxiv:2112.05273"},{"key":"1310_CR13","doi-asserted-by":"publisher","unstructured":"Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to interval analysis. Soc. Ind. Appl. Math. (2009). https:\/\/doi.org\/10.1137\/1.9780898717716","DOI":"10.1137\/1.9780898717716"},{"key":"1310_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-9093-7","volume-title":"Simplicial Global Optimization","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J.: Simplicial Global Optimization. Springer, New York (2014)"},{"key":"1310_CR15","doi-asserted-by":"crossref","unstructured":"Rall, L.B. (ed.): Examples of software for automatic differentiation and generation of Taylor coefficients, pp. 54\u201390. Springer, Berlin (1981)","DOI":"10.1007\/3-540-10861-0_5"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-023-01310-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-023-01310-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-023-01310-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,15]],"date-time":"2025-02-15T05:47:56Z","timestamp":1739598476000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-023-01310-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,11]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["1310"],"URL":"https:\/\/doi.org\/10.1007\/s10898-023-01310-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2023,7,11]]},"assertion":[{"value":"17 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The manuscript has no associated data. The used test instances are referenced in the text.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Statements and Declarations"}}]}}