{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:26:28Z","timestamp":1763389588524,"version":"3.37.3"},"reference-count":84,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100010909","name":"Young Scientists Fund","doi-asserted-by":"publisher","award":["11601327"],"award-info":[{"award-number":["11601327"]}],"id":[{"id":"10.13039\/501100010909","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10915-022-01882-z","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T13:13:51Z","timestamp":1656594831000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Discrete Dynamical System Approaches for Boolean Polynomial Optimization"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9993-3681","authenticated-orcid":false,"given":"Yi-Shuai","family":"Niu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roland","family":"Glowinski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"issue":"1","key":"1882_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-008-0001-1","volume":"1","author":"T Achterberg","year":"2009","unstructured":"Achterberg, T.: Scip: solving constraint integer programs. Math. Program. Comput. 1(1), 1\u201341 (2009)","journal-title":"Math. Program. Comput."},{"key":"1882_CR2","doi-asserted-by":"crossref","unstructured":"Amit, D.J.: Modeling brain function: The world of attractor neural networks. Cambridge University Press (1989)","DOI":"10.1017\/CBO9780511623257"},{"key":"1882_CR3","first-page":"5136","volume":"258","author":"E Balas","year":"1964","unstructured":"Balas, E.: Extension de l\u2019algorithme additif \u00e0 la programmation en nombres entiers et \u00e0 la programmation non lin\u00e9aire. C. R. Hebd. Seances Acad. Sci. 258, 5136\u20135139 (1964)","journal-title":"C. R. Hebd. Seances Acad. Sci."},{"issue":"4","key":"1882_CR4","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1287\/opre.13.4.517","volume":"13","author":"E Balas","year":"1965","unstructured":"Balas, E.: An additive algorithm for solving linear programs with zero-one variables. Oper. Res. 13(4), 517\u2013546 (1965)","journal-title":"Oper. Res."},{"issue":"1","key":"1882_CR5","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1287\/opre.19.1.19","volume":"19","author":"E Balas","year":"1971","unstructured":"Balas, E.: Intersection cuts - a new type of cutting planes for integer programming. Oper. Res. 19(1), 19\u201339 (1971)","journal-title":"Oper. Res."},{"key":"1882_CR6","doi-asserted-by":"crossref","unstructured":"Balas, E., Ceria, S., Cornu\u00e9jols, G.: A lift-and-project cutting plane algorithm for mixed 0\u20131 programs. Math. Program. 58(1\u20133), 295\u2013324 (1993)","DOI":"10.1007\/BF01581273"},{"issue":"4\u20135","key":"1882_CR7","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1080\/10556780903087124","volume":"24","author":"P Belotti","year":"2009","unstructured":"Belotti, P., Lee, J., Liberti, L., Margot, F., W\u00e4chter, A.: Branching and bounds tighteningtechniques for non-convex minlp. Optimization Methods & Software 24(4\u20135), 597\u2013634 (2009)","journal-title":"Optimization Methods & Software"},{"issue":"1","key":"1882_CR8","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"JF Benders","year":"1962","unstructured":"Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238\u2013252 (1962)","journal-title":"Numer. Math."},{"issue":"3","key":"1882_CR9","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1057\/palgrave.jors.2600425","volume":"48","author":"DP Bertsekas","year":"1997","unstructured":"Bertsekas, D.P.: Nonlinear programming. Journal of the Operational Research Society 48(3), 334 (1997)","journal-title":"Journal of the Operational Research Society"},{"key":"1882_CR10","first-page":"1","volume":"4","author":"P Bonami","year":"2007","unstructured":"Bonami, P., Lee, J.: Bonmin user\u2019s manual. Numer. Math. 4, 1\u201332 (2007)","journal-title":"Numer. Math."},{"issue":"1","key":"1882_CR11","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0166-218X(01)00341-9","volume":"123","author":"E Boros","year":"2002","unstructured":"Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Applied Mathematics 123(1), 155\u2013225 (2002)","journal-title":"Discrete Applied Mathematics"},{"issue":"1","key":"1882_CR12","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1137\/0901003","volume":"1","author":"J Bourgat","year":"1980","unstructured":"Bourgat, J., Dumay, J., Glowinski, R.: Large displacement calculations of flexible pipelines by finite element and nonlinear programming methods. SIAM J. Sci. Stat. Comput. 1(1), 34\u201381 (1980)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"1\u20134","key":"1882_CR13","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1023\/A:1019225027893","volume":"98","author":"A Caprara","year":"2000","unstructured":"Caprara, A., Toth, P., Fischetti, M.: Algorithms for the set covering problem. Ann. Oper. Res. 98(1\u20134), 353\u2013371 (2000)","journal-title":"Ann. Oper. Res."},{"issue":"13","key":"1882_CR14","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1016\/S0305-0548(99)00074-X","volume":"27","author":"TJ Chang","year":"2000","unstructured":"Chang, T.J., Meade, N., Beasley, J.E., Sharaiha, Y.M.: Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research 27(13), 1271\u20131302 (2000)","journal-title":"Computers & Operations Research"},{"issue":"3","key":"1882_CR15","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1287\/moor.4.3.233","volume":"4","author":"V Chvatal","year":"1979","unstructured":"Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233\u2013235 (1979)","journal-title":"Math. Oper. Res."},{"key":"1882_CR16","unstructured":"COIN-OR: Open source for the operations research community. https:\/\/www.coin-or.org\/"},{"issue":"5","key":"1882_CR17","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1057\/jors.1992.75","volume":"43","author":"D Connolly","year":"1992","unstructured":"Connolly, D.: General purpose simulated annealing. Journal of the Operational Research Society 43(5), 495\u2013505 (1992)","journal-title":"Journal of the Operational Research Society"},{"issue":"1","key":"1882_CR18","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-006-0086-0","volume":"112","author":"G Cornu\u00e9jols","year":"2008","unstructured":"Cornu\u00e9jols, G.: Valid inequalities for mixed integer linear programs. Math. Program. 112(1), 3\u201344 (2008)","journal-title":"Math. Program."},{"issue":"4","key":"1882_CR19","first-page":"393","volume":"2","author":"GB Dantzig","year":"1954","unstructured":"Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: Solution of a large-scale traveling-salesman problem. J. Oper. Res. Soc. Am. 2(4), 393\u2013410 (1954)","journal-title":"J. Oper. Res. Soc. Am."},{"issue":"1","key":"1882_CR20","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1287\/opre.7.1.58","volume":"7","author":"GB Dantzig","year":"1959","unstructured":"Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: On a linear-programming, combinatorial approach to the traveling-salesman problem. Oper. Res. 7(1), 58\u201366 (1959)","journal-title":"Oper. Res."},{"key":"1882_CR21","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1023\/A:1018952112615","volume":"86","author":"JV De Carvalho","year":"1999","unstructured":"De Carvalho, J.V.: Exact solution of bin-packing problems using column generation and branch-and-bound. Ann. Oper. Res. 86, 629\u2013659 (1999)","journal-title":"Ann. Oper. Res."},{"issue":"1\u20133","key":"1882_CR22","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/BF01585184","volume":"62","author":"C Delorme","year":"1993","unstructured":"Delorme, C., Poljak, S.: Laplacian eigenvalues and the maximum cut problem. Math. Program. 62(1\u20133), 557\u2013574 (1993)","journal-title":"Math. Program."},{"issue":"2","key":"1882_CR23","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1162\/106454699568728","volume":"5","author":"M Dorigo","year":"1999","unstructured":"Dorigo, M., Caro, G.D., Gambardella, L.M.: Ant algorithms for discrete optimization. Artif. Life 5(2), 137\u2013172 (1999)","journal-title":"Artif. Life"},{"issue":"1","key":"1882_CR24","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","volume":"6","author":"JR Dormand","year":"1980","unstructured":"Dormand, J.R., Prince, P.J.: A family of embedded runge-kutta formulae. J. Comput. Appl. Math. 6(1), 19\u201326 (1980)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"1882_CR25","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1287\/ijoc.2017.0798","volume":"30","author":"I Dunning","year":"2018","unstructured":"Dunning, I., Gupta, S., Silberholz, J.: What works best when? a systematic evaluation of heuristics for max-cut and qubo. INFORMS J. Comput. 30(3), 608\u2013624 (2018)","journal-title":"INFORMS J. Comput."},{"issue":"3","key":"1882_CR26","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1287\/opre.14.3.361","volume":"14","author":"M Efroymson","year":"1966","unstructured":"Efroymson, M., Ray, T.: A branch-bound algorithm for plant location. Oper. Res. 14(3), 361\u2013368 (1966)","journal-title":"Oper. Res."},{"issue":"5","key":"1882_CR27","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1287\/opre.42.5.860","volume":"42","author":"TA Feo","year":"1994","unstructured":"Feo, T.A., Resende, M.G., Smith, S.H.: A greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 42(5), 860\u2013878 (1994)","journal-title":"Oper. Res."},{"key":"1882_CR28","unstructured":"Fico: Fico xpress optimization. https:\/\/www.fico.com\/"},{"key":"1882_CR29","unstructured":"Forrest, J.: Cbc (coin-or branch and cut) open-source mixed integer programming solver. https:\/\/projects.coin-or.org\/Cbc (2012)"},{"key":"1882_CR30","unstructured":"Fran\u00e7a, G., Robinson, D.P., Vidal, R.: Admm and accelerated admm as continuous dynamical systems. In: International Conference on Machine Learning, pp. 1559\u20131567. PMLR (2018)"},{"issue":"5","key":"1882_CR31","doi-asserted-by":"publisher","first-page":"053304","DOI":"10.1103\/PhysRevE.103.053304","volume":"103","author":"G Fran\u00e7a","year":"2021","unstructured":"Fran\u00e7a, G., Robinson, D.P., Vidal, R.: Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization. Phys. Rev. E 103(5), 053304 (2021)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"1882_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-2217(03)00274-1","volume":"155","author":"A Fr\u00e9ville","year":"2004","unstructured":"Fr\u00e9ville, A.: The multidimensional 0\u20131 knapsack problem: An overview. Eur. J. Oper. Res. 155(1), 1\u201321 (2004)","journal-title":"Eur. J. Oper. Res."},{"issue":"3","key":"1882_CR33","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1287\/opre.2013.1170","volume":"61","author":"J Gao","year":"2013","unstructured":"Gao, J., Li, D.: Optimal cardinality constrained portfolio selection. Oper. Res. 61(3), 745\u2013761 (2013)","journal-title":"Oper. Res."},{"key":"1882_CR34","doi-asserted-by":"crossref","unstructured":"Gen, M., Lin, L.: Genetic algorithms. Wiley Encyclopedia of Computer Science and Engineering pp. 1\u201315 (2007)","DOI":"10.1002\/9780470050118.ecse169"},{"issue":"3","key":"1882_CR35","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1287\/opre.17.3.437","volume":"17","author":"AM Geoffrion","year":"1969","unstructured":"Geoffrion, A.M.: An improved implicit enumeration approach for integer programming. Oper. Res. 17(3), 437\u2013454 (1969)","journal-title":"Oper. Res."},{"issue":"4","key":"1882_CR36","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1287\/mnsc.22.4.455","volume":"22","author":"F Glover","year":"1975","unstructured":"Glover, F.: Improved linear integer programming formulations of nonlinear integer problems. Manage. Sci. 22(4), 455\u2013460 (1975)","journal-title":"Manage. Sci."},{"issue":"5","key":"1882_CR37","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1016\/0305-0548(86)90048-1","volume":"13","author":"F Glover","year":"1986","unstructured":"Glover, F.: Future paths for integer programming and links to artificial intelligence. Computers & operations research 13(5), 533\u2013549 (1986)","journal-title":"Computers & operations research"},{"issue":"1","key":"1882_CR38","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1287\/opre.22.1.180","volume":"22","author":"F Glover","year":"1974","unstructured":"Glover, F., Woolsey, E.: Converting the 0\u20131 polynomial programming problem to a 0\u20131 linear program. Oper. Res. 22(1), 180\u2013182 (1974)","journal-title":"Oper. Res."},{"key":"1882_CR39","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Osher, S.J., Yin, W.: Splitting methods in communication, imaging, science, and engineering. Springer (2017)","DOI":"10.1007\/978-3-319-41589-5"},{"issue":"6","key":"1882_CR40","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"MX Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM (JACM) 42(6), 1115\u20131145 (1995)","journal-title":"Journal of the ACM (JACM)"},{"issue":"5","key":"1882_CR41","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1090\/S0002-9904-1958-10224-4","volume":"64","author":"RE Gomory","year":"1958","unstructured":"Gomory, R.E., et al.: Outline of an algorithm for integer solutions to linear programs. Bull. Am. Math. Soc. 64(5), 275\u2013278 (1958)","journal-title":"Bull. Am. Math. Soc."},{"key":"1882_CR42","unstructured":"Gurobi: Gurobi 8.1. http:\/\/www.gurobi.com\/"},{"issue":"4","key":"1882_CR43","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/BF02241270","volume":"44","author":"P Hansen","year":"1990","unstructured":"Hansen, P., Jaumard, B.: Algorithms for the maximum satisfiability problem. Computing 44(4), 279\u2013303 (1990)","journal-title":"Computing"},{"issue":"1\u20133","key":"1882_CR44","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF02614317","volume":"79","author":"P Hansen","year":"1997","unstructured":"Hansen, P., Jaumard, B.: Cluster analysis and mathematical programming. Math. Program. 79(1\u20133), 191\u2013215 (1997)","journal-title":"Math. Program."},{"key":"1882_CR45","unstructured":"IBM: Ibm ilog cplex optimization studio v12.9.0 documentation"},{"key":"1882_CR46","doi-asserted-by":"crossref","unstructured":"J\u00fcnger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A.: 50 Years of integer programming 1958-2008: From the early years to the state-of-the-art. Springer Science & Business Media (2009)","DOI":"10.1007\/978-3-540-68279-0"},{"key":"1882_CR47","doi-asserted-by":"crossref","unstructured":"Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of computer computations, pp. 85\u2013103. Springer (1972)","DOI":"10.1007\/978-1-4684-2001-2_9"},{"issue":"9","key":"1882_CR48","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1287\/mnsc.13.9.723","volume":"13","author":"PJ Kolesar","year":"1967","unstructured":"Kolesar, P.J.: A branch and bound algorithm for the knapsack problem. Manage. Sci. 13(9), 723\u2013735 (1967)","journal-title":"Manage. Sci."},{"issue":"2","key":"1882_CR49","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1287\/moor.27.2.347.322","volume":"27","author":"JB Lasserre","year":"2002","unstructured":"Lasserre, J.B.: Semidefinite programming vs. lp relaxations for polynomial programming. Mathematics of operations research 27(2), 347\u2013360 (2002)","journal-title":"Mathematics of operations research"},{"issue":"3","key":"1882_CR50","first-page":"1","volume":"45","author":"HA Le Thi","year":"2001","unstructured":"Le Thi, H.A., Pham, D.T.: A continuous approach for large-scale constrained quadratic zero-one programming. Optimization 45(3), 1\u201328 (2001)","journal-title":"Optimization"},{"issue":"4","key":"1882_CR51","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10287-009-0098-3","volume":"6","author":"HA Le Thi","year":"2009","unstructured":"Le Thi, H.A., Moeini, M., Pham, D.T.: Portfolio selection under downside risk measures and cardinality constraints based on dc programming and dca. CMS 6(4), 459\u2013475 (2009)","journal-title":"CMS"},{"issue":"1","key":"1882_CR52","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1111\/j.1467-9965.2006.00262.x","volume":"16","author":"D Li","year":"2006","unstructured":"Li, D., Sun, X., Wang, J.: Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics 16(1), 83\u2013101 (2006)","journal-title":"Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics"},{"key":"1882_CR53","unstructured":"L\u00f6fberg, J.: Yalmip: A toolbox for modeling and optimization in matlab. In: Proceedings of the CACSD Conference, vol.\u00a03. Taipei, Taiwan (2004)"},{"issue":"2\u20133","key":"1882_CR54","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1016\/S0377-2217(97)00295-6","volume":"106","author":"A Lokketangen","year":"1998","unstructured":"Lokketangen, A., Glover, F.: Solving zero-one mixed integer programming problems using tabu search. Eur. J. Oper. Res. 106(2\u20133), 624\u2013658 (1998)","journal-title":"Eur. J. Oper. Res."},{"issue":"3\u20134","key":"1882_CR55","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0305-0548(92)90044-6","volume":"19","author":"CK Looi","year":"1992","unstructured":"Looi, C.K.: Neural network methods in combinatorial optimization. Computers & Operations Research 19(3\u20134), 191\u2013208 (1992)","journal-title":"Computers & Operations Research"},{"issue":"2","key":"1882_CR56","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1137\/0801013","volume":"1","author":"L Lov\u00e1sz","year":"1991","unstructured":"Lov\u00e1sz, L., Schrijver, A.: Cones of matrices and set-functions and 0\u20131 optimization. SIAM J. Optim. 1(2), 166\u2013190 (1991)","journal-title":"SIAM J. Optim."},{"key":"1882_CR57","unstructured":"Makhorin, A.: Gnu linear programming kit. Moscow Aviation Institute, Moscow, Russia 38 (2001)"},{"key":"1882_CR58","unstructured":"Man Jr, E.C., Garey, M., Johnson, D.: Approximation algorithms for bin packing: A survey. Approximation algorithms for NP-hard problems pp. 46\u201393 (1996)"},{"issue":"1","key":"1882_CR59","first-page":"77","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz, H.: Portfolio selection. The journal of finance 7(1), 77\u201391 (1952)","journal-title":"The journal of finance"},{"key":"1882_CR60","unstructured":"MathWorks: Matlab documentation. http:\/\/www.mathworks.com\/help\/matlab\/"},{"key":"1882_CR61","unstructured":"Moder, J.J., Phillips, C.R., Davis, E.W.: Project management with CPM, PERT, and precedence diagramming. Van Nostrand Reinhold New York (1983)"},{"key":"1882_CR62","unstructured":"Mosek, A.: The mosek optimization software. http:\/\/www.mosek.com"},{"key":"1882_CR63","doi-asserted-by":"crossref","unstructured":"Niu, Y.S., Hu, X.W., You, Y., Benammour, F.M., Zhang, H.: Sentence compression via dc programming approach. In: World Congress on Global Optimization, pp. 341\u2013351. Springer (2019)","DOI":"10.1007\/978-3-030-21803-4_35"},{"key":"1882_CR64","doi-asserted-by":"crossref","unstructured":"Niu, Y.S., Pham, D.T.: A dc programming approach for mixed-integer linear programs. In: International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 244\u2013253. Springer (2008)","DOI":"10.1007\/978-3-540-87477-5_27"},{"key":"1882_CR65","doi-asserted-by":"crossref","unstructured":"Niu, Y.S., You, Y., Liu, W.Z.: Parallel dc cutting plane algorithms for mixed binary linear program. In: World Congress on Global Optimization, pp. 330\u2013340. Springer (2019)","DOI":"10.1007\/978-3-030-21803-4_34"},{"key":"1882_CR66","unstructured":"Niu, Y.S.: Demipp \u2013 a matlab toolbox of differential equation methods for integer polynomial programs. https:\/\/github.com\/niuyishuai\/DEMIPP"},{"key":"1882_CR67","unstructured":"Niu, Y.S.: On difference-of-sos and difference-of-convex-sos decompositions for polynomials. Preprint arXiv:1803.09900 (2018)"},{"key":"1882_CR68","unstructured":"Niu, Y.S.: Polylab \u2013 a matlab multivariate polynomial toolbox. https:\/\/github.com\/niuyishuai\/Polylab"},{"key":"1882_CR69","unstructured":"Niu, Y.S.: Programmation dc & dca en optimisation combinatoire et optimisation polynomiale via les techniques de sdp. Ph.D. thesis, INSA de Rouen, France (2010)"},{"key":"1882_CR70","doi-asserted-by":"crossref","unstructured":"Pardalos, P.M., Mavridou, T., Xue, J.: The graph coloring problem: A bibliographic survey. In: Handbook of combinatorial optimization, pp. 1077\u20131141. Springer (1998)","DOI":"10.1007\/978-1-4613-0303-9_16"},{"issue":"2","key":"1882_CR71","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","volume":"96","author":"PA Parrilo","year":"2003","unstructured":"Parrilo, P.A.: Semidefinite programming relaxations for semialgebraic problems. Math. Program. 96(2), 293\u2013320 (2003)","journal-title":"Math. Program."},{"issue":"5","key":"1882_CR72","doi-asserted-by":"publisher","first-page":"4217","DOI":"10.1103\/PhysRevA.34.4217","volume":"34","author":"L Personnaz","year":"1986","unstructured":"Personnaz, L., Guyon, I., Dreyfus, G.: Collective computational properties of neural networks: New learning mechanisms. Phys. Rev. A 34(5), 4217 (1986)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"1882_CR73","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s11590-015-0931-2","volume":"10","author":"DT Pham","year":"2016","unstructured":"Pham, D.T., Le Thi, H.A., Pham, V.N., Niu, Y.S.: Dc programming approaches for discrete portfolio optimization under concave transaction costs. Optimization Letters 10(2), 261\u2013282 (2016)","journal-title":"Optimization Letters"},{"issue":"5","key":"1882_CR74","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0041-5553(64)90137-5","volume":"4","author":"BT Polyak","year":"1964","unstructured":"Polyak, B.T.: Some methods of speeding up the convergence of iteration methods. USSR Comput. Math. Math. Phys. 4(5), 1\u201317 (1964)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"1882_CR75","unstructured":"Robinson, J.: On the hamiltonian game (a traveling salesman problem). Rand Corporation (1949)"},{"issue":"2","key":"1882_CR76","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/BF00138693","volume":"8","author":"NV Sahinidis","year":"1996","unstructured":"Sahinidis, N.V.: Baron: A general purpose global optimization software package. J. Global Optim. 8(2), 201\u2013205 (1996)","journal-title":"J. Global Optim."},{"key":"1882_CR77","unstructured":"Schrage, L.E., LINDO\u00a0Systems, I.: Optimization modeling with LINGO. Duxbury Press CA (1997)"},{"issue":"1","key":"1882_CR78","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S1064827594276424","volume":"18","author":"LF Shampine","year":"1997","unstructured":"Shampine, L.F., Reichelt, M.W.: The matlab ode suite. SIAM J. Sci. Comput. 18(1), 1\u201322 (1997)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1882_CR79","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"HD Sherali","year":"1990","unstructured":"Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discret. Math. 3(3), 411\u2013430 (1990)","journal-title":"SIAM J. Discret. Math."},{"issue":"1","key":"1882_CR80","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1287\/ijoc.11.1.15","volume":"11","author":"KA Smith","year":"1999","unstructured":"Smith, K.A.: Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J. Comput. 11(1), 15\u201334 (1999)","journal-title":"INFORMS J. Comput."},{"issue":"1","key":"1882_CR81","first-page":"2510","volume":"3","author":"W Su","year":"2015","unstructured":"Su, W., Boyd, S., Candes, E.J.: A differential equation for modeling nesterov\u2019s accelerated gradient method: Theory and insights. Adv. Neural. Inf. Process. Syst. 3(1), 2510\u20132518 (2015)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"3","key":"1882_CR82","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1137\/0206038","volume":"6","author":"RE Tarjan","year":"1977","unstructured":"Tarjan, R.E., Trojanowski, A.E.: Finding a maximum independent set. SIAM J. Comput. 6(3), 537\u2013546 (1977)","journal-title":"SIAM J. Comput."},{"key":"1882_CR83","doi-asserted-by":"crossref","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming 106(1), 25\u201357 (2006). URL https:\/\/github.com\/coin-or\/Ipopt","DOI":"10.1007\/s10107-004-0559-y"},{"issue":"6","key":"1882_CR84","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1287\/opre.15.6.1171","volume":"15","author":"LJ Watters","year":"1967","unstructured":"Watters, L.J.: Letter to the editor-reduction of integer polynomial programming problems to zero-one linear programming problems. Oper. Res. 15(6), 1171\u20131174 (1967)","journal-title":"Oper. Res."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01882-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-022-01882-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01882-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,23]],"date-time":"2022-10-23T23:20:06Z","timestamp":1666567206000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-022-01882-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,30]]},"references-count":84,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["1882"],"URL":"https:\/\/doi.org\/10.1007\/s10915-022-01882-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2022,6,30]]},"assertion":[{"value":"1 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Inquiries about data availability should be directed to the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Data Availability"}},{"value":"Our code DEMIPP is available at .","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code Availability"}}],"article-number":"46"}}