{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T06:49:15Z","timestamp":1742971755669,"version":"3.40.3"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030910587"},{"type":"electronic","value":"9783030910594"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-91059-4_8","type":"book-chapter","created":{"date-parts":[[2021,11,4]],"date-time":"2021-11-04T15:02:57Z","timestamp":1636038177000},"page":"110-120","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Search for All Roots of a System of\u00a0Quadratic Equations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4579-3927","authenticated-orcid":false,"given":"Tatiana V.","family":"Gruzdeva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oleg V.","family":"Khamisov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,5]]},"reference":[{"issue":"2","key":"8_CR1","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F., Falk, J.: Jointly constrained biconvex programming. Math. Oper. Res. 8(2), 273\u2013286 (1983)","journal-title":"Math. Oper. Res."},{"key":"8_CR2","series-title":"SEMA SIMAI Springer Series","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-39228-8","volume-title":"Advances in Iterative Methods for Nonlinear Equations","year":"2016","unstructured":"Amat, S., Busquier, S. (eds.): Advances in Iterative Methods for Nonlinear Equations. SEMA SIMAI, vol. 10. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-39228-8"},{"issue":"5","key":"8_CR3","doi-asserted-by":"publisher","first-page":"3608","DOI":"10.1137\/08073264X","volume":"47","author":"D Bates","year":"2009","unstructured":"Bates, D., Hauenstein, J., Peterson, C., Sommese, A.: A numerical local dimension test for points on the solution set of a system of polynomial equations. SIAM J. Numer. Anal. 47(5), 3608\u20133623 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"8_CR4","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/BF02283699","volume":"25","author":"V Bulatov","year":"1990","unstructured":"Bulatov, V.: Methods for solving multi-extremal problems (global search). Ann. Oper. Res. 25, 253\u2013277 (1990)","journal-title":"Ann. Oper. Res."},{"key":"8_CR5","first-page":"331","volume":"40","author":"V Bulatov","year":"2000","unstructured":"Bulatov, V.: Numerical method of funding all real roots of systems of nonlinear equations. Comput. Math. Math. Phys. 40, 331\u2013338 (2000)","journal-title":"Comput. Math. Math. Phys."},{"key":"8_CR6","series-title":"Undergraduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-16721-3","volume-title":"Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"DA Cox","year":"2015","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. UTM, Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-16721-3"},{"key":"8_CR7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971200","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equation","author":"JE Dennis","year":"1996","unstructured":"Dennis, J.E., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equation. SIAM, Philadelphia (1996)"},{"key":"8_CR8","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/b138957","volume-title":"Solving Polynomial Equations. Foundations, Algorithms, and Applications","year":"2005","unstructured":"Dickenstein, A., Emiris, I. (eds.): Solving Polynomial Equations. Foundations, Algorithms, and Applications. AACIM, vol. 14. Springer-Verlag, Heidelberg (2005). https:\/\/doi.org\/10.1007\/b138957"},{"key":"8_CR9","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s00186-012-0419-0","volume":"77","author":"F Facchinei","year":"2013","unstructured":"Facchinei, F., Fischer, A., Herrich, M.: A family of newton methods for nonsmooth constrained systems with nonisolated solutions. Math. Meth. Oper. Res. 77, 433\u2013443 (2013)","journal-title":"Math. Meth. Oper. Res."},{"issue":"4","key":"8_CR10","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1109\/TSMC.2018.2828018","volume":"50","author":"W Gong","year":"2020","unstructured":"Gong, W., Wang, Y., Cai, Z., Wang, L.: Finding multiple roots of nonlinear equation systems via a repulsion-based adaptive differential evolution. IEEE Trans. Syst. Man Cybern. Syst. 50(4), 1499\u20131513 (2020)","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"3","key":"8_CR11","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1134\/S0965542507030049","volume":"47","author":"TV Gruzdeva","year":"2007","unstructured":"Gruzdeva, T.V., Strekalovsky, A.S.: Local search in problems with nonconvex constraints. Comput. Math. Math. Phys. 47(3), 381\u2013396 (2007)","journal-title":"Comput. Math. Math. Phys."},{"issue":"4","key":"8_CR12","doi-asserted-by":"publisher","first-page":"2000","DOI":"10.1016\/j.nonrwa.2008.03.006","volume":"10","author":"M Hirsch","year":"2009","unstructured":"Hirsch, M., Pardalos, P., Resende, M.: Solving systems of nonlinear equations with continuous grasp. Nonlinear Anal. Real World Appl. 10(4), 2000\u20132006 (2009)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"8_CR13","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10107-017-1128-5","volume":"167","author":"A Izmailov","year":"2018","unstructured":"Izmailov, A., Kurennoy, A., Solodov, M.: Critical solutions of nonlinear equations: local attraction for newton type-methods. Math. Program. 167, 355\u2013379 (2018)","journal-title":"Math. Program."},{"key":"8_CR14","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"C Kelley","year":"1995","unstructured":"Kelley, C.: Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia (1995)"},{"key":"8_CR15","doi-asserted-by":"publisher","first-page":"042007","DOI":"10.1088\/1757-899X\/537\/4\/042007","volume":"537","author":"O Khamisov","year":"2019","unstructured":"Khamisov, O., Kolosnitsyn, A.: An optimization approach to finding roots of systems of nonlinear equations. IOP Conf. Ser. Mater. Sci. Eng. 537, 042007 (2019)","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"issue":"1","key":"8_CR16","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"GP McCormick","year":"1976","unstructured":"McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part i-convex underestimating problems. Math. Program. 10(1), 147\u2013175 (1976)","journal-title":"Math. Program."},{"key":"8_CR17","series-title":"Power Systems","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13669-6","volume-title":"Power System Modelling and Scripting","author":"F Milano","year":"2010","unstructured":"Milano, F.: Power System Modelling and Scripting. POWSYS, Springer-Verlag, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13669-6"},{"key":"8_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-35447-5","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006). https:\/\/doi.org\/10.1007\/978-3-540-35447-5"},{"key":"8_CR19","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"J Ortega","year":"1970","unstructured":"Ortega, J., Rheinboldt, W.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)"},{"issue":"1","key":"8_CR20","doi-asserted-by":"publisher","first-page":"21","DOI":"10.18576\/amis\/120102","volume":"12","author":"G Ramadas","year":"2018","unstructured":"Ramadas, G., Fernandes, E., Rocha, A.: Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method. Appl. Math. Inf. Sci. 12(1), 21\u201332 (2018)","journal-title":"Appl. Math. Inf. Sci."},{"key":"8_CR21","unstructured":"Roose, A., Kulla, V., Lomp, M., Meressoo, T.: Test Examples of Systems of Non-linear Equations. Estonian Software and Computer Service Company, Tallin (1990)"},{"issue":"1","key":"8_CR22","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1137\/S0036142902418898","volume":"42","author":"H Schichl","year":"2004","unstructured":"Schichl, H., Neumaier, A.: Exclusion regions for systems of equations. SIAM J. Numer. Anal. 42(1), 383\u2013408 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"8_CR23","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/s10559-015-9775-0","volume":"51","author":"VY Semenov","year":"2015","unstructured":"Semenov, V.Y.: A method to find all the roots of the system of nonlinear algebraic equations based on the krawczyk operator. Cybern. Syst. Anal. 51, 819\u2013825 (2015)","journal-title":"Cybern. Syst. Anal."},{"key":"8_CR24","doi-asserted-by":"publisher","first-page":"1428","DOI":"10.1134\/S0965542507090047","volume":"47","author":"V Semenov","year":"2007","unstructured":"Semenov, V.: The method of determining all real nonmultiple roots of systems of nonlinear equations. Comput. Math. Math. Phys. 47, 1428\u20131434 (2007)","journal-title":"Comput. Math. Math. Phys."},{"key":"8_CR25","unstructured":"Shary, S.: Finite-dimensional interval analysis. XYZ, Novosibirsk (2020)"},{"key":"8_CR26","doi-asserted-by":"crossref","unstructured":"Stetter, H.: Numerical Polynomial Algebra. SIAM, New York (2004)","DOI":"10.1137\/1.9780898717976"},{"key":"8_CR27","doi-asserted-by":"crossref","unstructured":"Strekalovsky, A.S.: On local search in d.c. optimization problems. Appl. Math. Comput. 255, 73\u201383 (2015)","DOI":"10.1016\/j.amc.2014.08.092"},{"issue":"2","key":"8_CR28","first-page":"23","volume":"133","author":"PD Tao","year":"2005","unstructured":"Tao, P.D., An, L.T.H.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133(2), 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"issue":"4","key":"8_CR29","doi-asserted-by":"publisher","first-page":"2465","DOI":"10.1016\/j.nonrwa.2009.08.003","volume":"11","author":"I Tsoulos","year":"2010","unstructured":"Tsoulos, I., Stavrakoudis, A.: On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods. Nonlinear Anal. Real World Appl. 11(4), 2465\u20132471 (2010)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"8_CR30","doi-asserted-by":"crossref","unstructured":"Wang, W.-X., Shang, Y.-L., Wang, G.S., Zhang, Y.: Finding the roots of system of nonlinear equations by a novel filled function method. Abstract Appl. Anal. 2011. Article ID 209083 (2011)","DOI":"10.1155\/2011\/209083"},{"issue":"1\u20132","key":"8_CR31","first-page":"587","volume":"152","author":"K Yamamura","year":"2004","unstructured":"Yamamura, K., Fujioka, T.: Finding all solutions of nonlinear equations using the dual simplex method. J. Comput. Appl. Math. 152(1\u20132), 587\u2013595 (2004)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Lecture Notes in Computer Science","Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-91059-4_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T23:03:41Z","timestamp":1638399821000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-91059-4_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030910587","9783030910594"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-91059-4_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"5 November 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"OPTIMA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Optimization and Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Petrovac","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montenegro","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"optima2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/agora.guru.ru\/display.php?conf=OPTIMA-2021","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"63","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"41","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"65% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.1","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}