{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:44Z","timestamp":1740144524749,"version":"3.37.3"},"reference-count":36,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T00:00:00Z","timestamp":1639699200000},"content-version":"vor","delay-in-days":46,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"NA","award":["NA"],"award-info":[{"award-number":["NA"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2021,11,30]]},"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p>In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. In improved algorithm we introduce several new ingredients, such as B-spline box consistency and B-spline hull consistency algorithm to prune the search regions and make the search more efficient. The performance of the basic and improved algorithm is tested and compared on set of test problems. The results of the tests show the superiority of the improved algorithm over the basic algorithm in terms of the chosen performance metrics for 7 out-off 11 test problems. We compare optimal value of global minimum obtained using the proposed algorithms with CENSO, GloptiPoly and several state-of-the-art NLP solvers, on set of 11 test problems. The results of the tests show the superiority of the proposed algorithm and CENSO solver (open source solver for global optimization of B-spline constrained problem) in that it always captures the global minimum to the user-specified accuracy.<\/jats:p>","DOI":"10.1051\/ro\/2021179","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T19:51:40Z","timestamp":1638388300000},"page":"3743-3771","source":"Crossref","is-referenced-by-count":2,"title":["Constrained global optimization of multivariate polynomials using polynomial B-spline form and B-spline consistency prune approach"],"prefix":"10.1051","volume":"55","author":[{"given":"Deepak D.","family":"Gawali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6992-8032","authenticated-orcid":false,"given":"Bhagyesh V.","family":"Patil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Zidna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. S. V.","family":"Nataraj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,12,17]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10107-009-0264-y","volume":"125","author":"Birgin","year":"2010","journal-title":"Math. Program."},{"key":"R2","unstructured":"Cloud M.J., Moore R.E. and Kearfott R.B., Introduction to Interval Analysis. Siam, Philadelphia (2009)."},{"key":"R3","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/0021-9045(72)90080-9","volume":"6","author":"De Boor","year":"1972","journal-title":"J. Approximation Theory"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"Floudas C.A. and Pardalos P.M., A Collection of Test Problems for Constrained Global Optimization Algorithms. Vol. 455. Springer (1990).","DOI":"10.1007\/3-540-53032-0"},{"key":"R5","unstructured":"Floudas C.A., Pardalos P.M., Adjiman C., Esposito W.R., G\u00fcm\u00fcs Z.H., Harding S.T., Klepeis J.L., Meyer C.A. and Schweiger C.A., Handbook of Test Problems in Local and Global Optimization. Springer Science & Business Media (2013)."},{"key":"R6","first-page":"154","volume":"6","author":"Garloff","year":"1993","journal-title":"Interval Comput."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Gawali D.D., Zidna A. and Nataraj P.S.V., Solving nonconvex optimization problems in systems and control: a polynomial B-spline approach. In: Modelling, Computation and Optimization in Information Systems and Management Sciences. Springer (2015) 467\u2013478.","DOI":"10.1007\/978-3-319-18161-5_40"},{"key":"R8","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cor.2017.02.013","volume":"87","author":"Gawali","year":"2017","journal-title":"Comput. Oper. Res."},{"key":"R9","doi-asserted-by":"crossref","unstructured":"Gawali D.D., Patil B.V., Zidna A. and Nataraj P.S.V., A B-spline global optimization algorithm for optimal power flow problem. In: World Congress on Global Optimization. Springer (2019) 58\u201367.","DOI":"10.1007\/978-3-030-21803-4_6"},{"key":"R10","unstructured":"Global library. available online at http:\/\/www.gamsworld.org\/global\/globallib."},{"key":"R11","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/s11590-017-1190-1","volume":"12","author":"Grimstad","year":"2018","journal-title":"Optim. Lett."},{"key":"R12","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s10898-020-00881-4","volume":"77","author":"Grimstad","year":"2020","journal-title":"J. Global Optim."},{"key":"R13","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10898-015-0358-4","volume":"65","author":"Grimstad","year":"2016","journal-title":"J. Global Optim."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"Hansen E. and Walster G., Global Optimization Using Interval Analysis, 2nd edition. Revised and Expanded. Vol. 264, Marcel DEKKER, INC., New York (2004).","DOI":"10.1201\/9780203026922"},{"key":"R15","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1145\/779359.779363","volume":"29","author":"Henrion","year":"2003","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"R16","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/MCS.2004.1299534","volume":"24","author":"Henrion","year":"2004","journal-title":"IEEE Control Syst. Mag."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Horst R. and Pardalos P.M., Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands (1995).","DOI":"10.1007\/978-1-4615-2025-2"},{"key":"R18","unstructured":"Jaulin L., Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Vol. 1. Springer Science & Business Media (2001)."},{"key":"R19","unstructured":"Kearfott R.B., Rigorous Global Search: Continuous Problems. Vol. 13, Springer Science & Business Media (2013)."},{"key":"R20","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"Lasserre","year":"2001","journal-title":"SIAM J. Optim."},{"key":"R21","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0377-0427(93)E0270-V","volume":"58","author":"Lin","year":"1995","journal-title":"J. Comput. Appl. Math."},{"key":"R22","first-page":"101","volume":"31","author":"Lin","year":"1996","journal-title":"Comput. Math. App."},{"key":"R23","unstructured":"Lyche T. and Morken K., Spline Methods Draft. Department of Informatics, Centre of Mathematics for Applications, University of Oslo (2008)."},{"key":"R24","unstructured":"Mathworks Inc., MATLAB version 8.0.0.783 (R 2012 b), Inc. Natick, Massachusetts, United States (2012)."},{"key":"R25","first-page":"85","volume":"233","author":"Michel","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"R26","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s12597-009-0009-y","volume":"46","author":"Nataraj","year":"2009","journal-title":"Opsearch"},{"key":"R27","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s10898-009-9485-0","volume":"49","author":"Nataraj","year":"2011","journal-title":"J. Global Optim."},{"key":"R28","unstructured":"NEOS Server for optimization. http:\/\/www.neos-server.org\/neos\/solvers\/ (2018)."},{"key":"R29","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.advengsoft.2011.09.009","volume":"45","author":"Park","year":"2012","journal-title":"Adv. Eng. Softw."},{"key":"R30","unstructured":"Patil B.V., Global optimization of polynomial mixed-integer nonlinear problems using the Bernstein form. Ph.D. thesis. Indian Institute of Technology, Bombay (2012)."},{"key":"R31","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s00607-011-0175-7","volume":"94","author":"Patil","year":"2012","journal-title":"Computing"},{"key":"R32","unstructured":"Ratschek H. and Rokne J., Computer Methods for the Range of Functions. Ellis Horwood Limited, Chichester, England (1984)."},{"key":"R33","unstructured":"Ratschek H. and Rokne J., New Computer Methods for Global Optimization. Ellis Horwood Limited, Chichester, England (1988)."},{"key":"R34","unstructured":"Shene C.K., CS3621 Introduction to computing with geometry notes. http:\/\/www.cs.mtu.edu\/shene\/COURSES\/cs3621\/NOTES\/ (2014)."},{"key":"R35","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/0098-1354(94)E0032-I","volume":"18","author":"Vaidyanathan","year":"1994","journal-title":"Comput. Chem. Eng."},{"key":"R36","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/S0036142995281504","volume":"34","author":"Van Hentenryck","year":"1997","journal-title":"SIAM J. Numer. Anal."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2021179\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T18:47:05Z","timestamp":1639766825000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2021179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11]]},"references-count":36,"journal-issue":{"issue":"6"},"alternative-id":["ro210272"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2021179","relation":{},"ISSN":["0399-0559","1290-3868"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"1290-3868"}],"subject":[],"published":{"date-parts":[[2021,11]]}}}