{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T11:31:54Z","timestamp":1763551914120},"reference-count":13,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2018,4,23]],"date-time":"2018-04-23T00:00:00Z","timestamp":1524441600000},"content-version":"vor","delay-in-days":112,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2018,1,31]]},"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this work, we propose a new underestimator in branch and bound algorithm for solving univariate global optimization problems. The new underestimator is a combination of two underestimators, the classical one used in <jats:italic>\u03b1<\/jats:italic>BB method (see Androulakis <jats:italic>et al.<\/jats:italic> [<jats:italic>J. Glob. Optim.<\/jats:italic> <jats:bold>7<\/jats:bold> (1995) 337\u20133637]) and the quadratic underestimator developed in Hoai An and Ouanes [<jats:italic>RAIRO: OR<\/jats:italic> <jats:bold>40<\/jats:bold> (2006) 285\u2013302]. We show that the new underestimator is tighter than the two underestimators. A convex\/concave test is used to accelerate the convergence of the proposed algorithm. The convergence of our algorithm is shown and a set of test problems given in Casado <jats:italic>et al.<\/jats:italic> [<jats:italic>J. Glob. Optim.<\/jats:italic> <jats:bold>25<\/jats:bold> (2003) 345\u2013362] are solved efficiently.<\/jats:p>","DOI":"10.1051\/ro\/2018013","type":"journal-article","created":{"date-parts":[[2018,2,2]],"date-time":"2018-02-02T19:50:12Z","timestamp":1517601012000},"page":"177-186","source":"Crossref","is-referenced-by-count":3,"title":["Combination of two underestimators for univariate global optimization"],"prefix":"10.1051","volume":"52","author":[{"given":"Mohand","family":"Ouanes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed","family":"Chebbah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Zidna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2018,4,23]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1016\/S0098-1354(98)00218-X","volume":"22","author":"Adjiman","year":"1998","journal-title":"Comput. 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