{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:36Z","timestamp":1760240376767,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T00:00:00Z","timestamp":1558569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The paper deals with the problem of global minimization of a polynomial function expressed through the Frobenius norm of two-dimensional or three-dimensional matrices. An adaptive procedure is proposed which applies a Multistart algorithm according to a heuristic approach. The basic step of the procedure consists of splitting the runs of different initial points in segments of fixed length and to interlace the processing order of the various segments, discarding those which appear less promising. A priority queue is suggested to implement this strategy. Various parameters contribute to the handling of the queue, whose length shrinks during the computation, allowing a considerable saving of the computational time with respect to classical procedures. To verify the validity of the approach, a large experimentation has been performed on both nonnegatively constrained and unconstrained problems.<\/jats:p>","DOI":"10.3390\/a12050109","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T02:22:00Z","timestamp":1558664520000},"page":"109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Adaptive Procedure for the Global Minimization of a Class of Polynomial Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0382-3195","authenticated-orcid":false,"given":"Paola","family":"Favati","sequence":"first","affiliation":[{"name":"Istituto di Informatica e Telematica (IIT\u2013CNR), Via G. 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Opt."},{"key":"ref_9","unstructured":"Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1992). Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press. [2nd ed.]."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0167-6377(99)00074-7","article-title":"On the convergence of the block nonlinear Gauss\u2013Seidel method under convex constraints","volume":"26","author":"Grippo","year":"2000","journal-title":"Oper. Res. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hsieh, C.J., and Dhillon, I.S. (2011, January 21\u201324). Fast coordinate descent methods with variable selection for non-negative matrix factorization. Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Diego, CA, USA.","DOI":"10.1145\/2020408.2020577"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s10898-014-0247-2","article-title":"SymNMF: Nonnegative low-rank approximation of a similarity matrix for graph clustering","volume":"62","author":"Kuang","year":"2015","journal-title":"J. Glob. Optim."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Favati, P., Lotti, G., Menchi, O., and Romani, F. (2019). 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