{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T22:49:11Z","timestamp":1779317351500,"version":"3.51.4"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s11075-022-01346-3","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T23:02:38Z","timestamp":1655938958000},"page":"1403-1424","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Finding global minima with an inflection point-based filled function algorithm"],"prefix":"10.1007","volume":"92","author":[{"given":"Ridwan","family":"Pandiya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salmah","family":"Salmah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Widodo","family":"Widodo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Irwan","family":"Endrayanto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"1346_CR1","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01585737","volume":"46","author":"R Ge","year":"1990","unstructured":"Ge, R.: A filled function method for finding a global minimizer of a function of several variables. Math. Program. 46, 191\u2013204 (1990)","journal-title":"Math. Program."},{"key":"1346_CR2","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1023\/A:1020243720794","volume":"24","author":"S Lucidi","year":"2002","unstructured":"Lucidi, S., Picialli, V.: New classes of globally convexized filled functions for global optimization. J. Global Optim. 24, 219\u2013236 (2002)","journal-title":"J. Global Optim."},{"key":"1346_CR3","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1023\/B:JOGO.0000006653.60256.f6","volume":"28","author":"LS Zhang","year":"2004","unstructured":"Zhang, L.S., Ng, C.K., Li, D., Tian, W.W.: A new filled function method for global optimization. J. Global Optim. 28, 17\u201343 (2004)","journal-title":"J. Global Optim."},{"key":"1346_CR4","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10957-004-1718-2","volume":"125","author":"ZY Wu","year":"2005","unstructured":"Wu, Z.Y., Zhang, L.S., Teo, K.L., Bai, F.S.: New modified function method for global optimization. J. Optim. Theory Appl. 125, 181\u2013203 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"1346_CR5","first-page":"501","volume":"173","author":"Y Yang","year":"2006","unstructured":"Yang, Y., Shang, Y.: A new filled function method for unconstrained global optimization. Appl. Math. Comput. 173, 501\u2013512 (2006)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR6","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1007\/s10957-013-0515-1","volume":"163","author":"F Wei","year":"2014","unstructured":"Wei, F., Wang, Y., Lin, H.: A new filled function method with two parameters for global optimization. J. Optim. Theory Appl. 163, 510\u2013527 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"1346_CR7","first-page":"685","volume":"268","author":"Y Gao","year":"2015","unstructured":"Gao, Y., Yang, Y., You, M.: A new filled function method for global optimization. Appl. Math. Comput. 268, 685\u2013695 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR8","first-page":"1246","volume":"273","author":"TM El-Gindy","year":"2016","unstructured":"El-Gindy, T.M., Salim, M.S., Ahmed, A.I.: A new filled function method applied to unconstrained global optimization. Appl. Math. Comput. 273, 1246\u20131256 (2016)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR9","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s11590-018-1315-1","volume":"13","author":"A Sahiner","year":"2019","unstructured":"Sahiner, A., Ibrahem, S.A.: A new global optimization technique by auxiliary function method in a directional search. Optim. Lett. 13, 309\u2013323 (2019)","journal-title":"Optim. Lett."},{"key":"1346_CR10","doi-asserted-by":"publisher","unstructured":"Jiahui, T., Wei, W., Yifan, X.: Lower-order smoothed objective penalty functions based on filling properties for constrained optimization problems. Optim. https:\/\/doi.org\/10.1080\/02331934.2020.1818746 (2020)","DOI":"10.1080\/02331934.2020.1818746"},{"key":"1346_CR11","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1023\/A:1011207512894","volume":"20","author":"Z Xu","year":"2001","unstructured":"Xu, Z., Huang, H.X., Pardalos, P.M., Xu, C.X.: Filled functions for unconstrained global optimization. J. Global Optim. 20, 49\u201365 (2001)","journal-title":"J. Global Optim."},{"key":"1346_CR12","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1023\/A:1008330632677","volume":"19","author":"X Liu","year":"2001","unstructured":"Liu, X.: Finding global minima with a computable filled function. J. Global Optim. 19, 151\u2013161 (2001)","journal-title":"J. Global Optim."},{"key":"1346_CR13","first-page":"745","volume":"151","author":"X Liu","year":"2004","unstructured":"Liu, X.: The impelling function method applied to global optimization. Appl. Math. Comput. 151, 745\u2013754 (2004)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR14","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0305-0548(02)00154-5","volume":"31","author":"X Liu","year":"2004","unstructured":"Liu, X., Xu, W.: A new filled function applied to global optimization. Comput. Oper. Res. 31, 61\u201380 (2004)","journal-title":"Comput. Oper. Res."},{"key":"1346_CR15","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.cam.2006.04.038","volume":"205","author":"YM Liang","year":"2007","unstructured":"Liang, Y.M., Zhang, L.S., Li, M.M., Han, B.S.: A filled function method for global optimization. J. Comput. Appl. Math. 205, 16\u201331 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"1346_CR16","first-page":"176","volume":"191","author":"YL Shang","year":"2007","unstructured":"Shang, Y.L., Pu, D.G., Jiang, A.P.: Finding global minimizer with one-parameter filled function on unconstrained global optimization. Appl. Math. Comput. 191, 176\u2013182 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR17","doi-asserted-by":"publisher","first-page":"1396","DOI":"10.1016\/j.mcm.2007.08.007","volume":"47","author":"YJ Wang","year":"2008","unstructured":"Wang, Y.J., Zhang, J.S.: A new constructing auxiliary function method for global optimization. Math. Comput. Model. 47, 1396\u20131410 (2008)","journal-title":"Math. Comput. Model."},{"key":"1346_CR18","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10898-010-9581-1","volume":"50","author":"Y Yang","year":"2011","unstructured":"Yang, Y., Bai, F.: An integral function and vector sequence method for unconstrained global optimization. J. Global Optim. 50, 293\u2013311 (2011)","journal-title":"J. Global Optim."},{"key":"1346_CR19","first-page":"3776","volume":"218","author":"H Lin","year":"2011","unstructured":"Lin, H., Wang, Y., Fan, L.: A filled function method with one parameter for unconstrained global optimization. Appl. Math. Comput. 218, 3776\u20133785 (2011)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR20","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s11075-013-9746-3","volume":"66","author":"H Lin","year":"2014","unstructured":"Lin, H., Gao, Y., Wang, Y.: A continuously differentiable filled function method for a global optimization. Numer. Algor. 66, 511\u2013523 (2014)","journal-title":"Numer. Algor."},{"key":"1346_CR21","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1007\/s11590-018-1275-5","volume":"13","author":"H Lin","year":"2019","unstructured":"Lin, H., Gao, Y., Wang, X., Su, S.: A filled function which has the same local minimizer of the objective function. Optim. Lett. 13, 761\u2013776 (2019)","journal-title":"Optim. Lett."},{"key":"1346_CR22","doi-asserted-by":"publisher","unstructured":"Wang, Z.Y., Yang, Y.J.: Novel global optimization algorithm with a space-filling curve and integral function. J. Oper. Res. Soc. China. https:\/\/doi.org\/10.1007\/s40305-020-00294-w (2021)","DOI":"10.1007\/s40305-020-00294-w"},{"key":"1346_CR23","first-page":"23","volume":"15","author":"X Sui","year":"2019","unstructured":"Sui, X., Wang, Y., Liu, J.: A new filled function method combining auxiliary function for global optimization. Pac. J. Optim. 15, 23\u201344 (2019)","journal-title":"Pac. J. Optim."},{"key":"1346_CR24","doi-asserted-by":"publisher","first-page":"2059011","DOI":"10.1142\/S0218001420590119","volume":"34","author":"J Liu","year":"2020","unstructured":"Liu, J., Wang, Y., Wei, S., Sui, X., Tong, W.: A filled flatten function method based on basin deepening and adaptive initial point for global optimization. Int. J. Pattern Recogn. 34, 2059011 (2020)","journal-title":"Int. J. Pattern Recogn."},{"key":"1346_CR25","doi-asserted-by":"publisher","first-page":"6234","DOI":"10.1007\/s10489-020-02179-0","volume":"51","author":"X Wu","year":"2021","unstructured":"Wu, X., Wang, Y., Fan, N.: A new filled function method based on adaptive search direction and valley widening for global optimization. Appl. Intell. 51, 6234\u20136254 (2021)","journal-title":"Appl. Intell."},{"key":"1346_CR26","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s11741-004-0024-4","volume":"8","author":"L An","year":"2004","unstructured":"An, L., Zhang, L., Chen, M.: A parameter-free filled function for unconstrained global optimization. J. Shanghai Univ. 8, 117\u2013123 (2004)","journal-title":"J. Shanghai Univ."},{"key":"1346_CR27","first-page":"3610","volume":"215","author":"S Ma","year":"2010","unstructured":"Ma, S., Yang, Y., Liu, H.: A parameter free filled function for unconstrained global optimization. Appl. Math. Comput. 215, 3610\u20133619 (2010)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR28","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10255-016-0560-2","volume":"32","author":"L Yuan","year":"2016","unstructured":"Yuan, L., Wan, Z., Tang, Q., Zheng, Y.: A class of parameter-free filled functions for box-constrained systems of nonlinear equations. Acta Math. Appl. Sin. Engl. Ser. 32, 355\u2013364 (2016)","journal-title":"Acta Math. Appl. Sin. Engl. Ser."},{"key":"1346_CR29","doi-asserted-by":"publisher","first-page":"2283","DOI":"10.1080\/00207160.2017.1283021","volume":"94","author":"H Liu","year":"2017","unstructured":"Liu, H., Wang, Y., Guan, S., Liu, X.: A new filled function method for unconstrained global optimization. Int. J. Comput. Math. 94, 2283\u20132296 (2017)","journal-title":"Int. J. Comput. Math."},{"key":"1346_CR30","first-page":"567","volume":"14","author":"H Liu","year":"2018","unstructured":"Liu, H., Wang, Y., Gao, X.Z., Dang, C., Meng, Z.: A parameter free filled function method for global optimization. Pac. J. Optim. 14, 567\u2013580 (2018)","journal-title":"Pac. J. Optim."},{"key":"1346_CR31","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1080\/00207160.2020.1731484","volume":"98","author":"AI Ahmed","year":"2021","unstructured":"Ahmed, A.I.: A new parameter free filled function for solving unconstrained global optimization problems. Int. J. Comput. Math. 98, 106\u2013119 (2021)","journal-title":"Int. J. Comput. Math."},{"key":"1346_CR32","first-page":"125642","volume":"391","author":"R Pandiya","year":"2021","unstructured":"Pandiya, R., Salmah, S, Widodo, W., Endrayanto, I.: Non parameter-filled function for global optimization. Appl. Math. Comput. 391, 125642 (2021)","journal-title":"Appl. Math. Comput."},{"key":"1346_CR33","unstructured":"Hedar, A.: Test functions for unconstrained global optimization. http:\/\/www-optima.amp.i.kyoto-u.ac.jp (2013). Accessed 2 October 2021"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01346-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-022-01346-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01346-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T08:32:39Z","timestamp":1673512359000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-022-01346-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,22]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["1346"],"URL":"https:\/\/doi.org\/10.1007\/s11075-022-01346-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,22]]},"assertion":[{"value":"12 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Competing interests"}}]}}