{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T16:38:31Z","timestamp":1772642311775,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:00:00Z","timestamp":1757980800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:00:00Z","timestamp":1757980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100006034","name":"University of Southern California","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100006034","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints (LPCCs). It is a classic result that for a QP with an optimal solution, the QP has an equivalent formulation as a certain LPCC in terms of their globally optimal solutions. Thus it is natural to attempt to solve an (indefinite) QP as a LPCC. This paper presents a progressive mixed integer linear programming method for solving a general LPCC. Instead of solving the LPCC with a full set of integer variables expressing the complementarity conditions, the presented method solves a finite number of mixed integer subprograms by starting with a small fraction of integer variables and progressively increasing this fraction. After describing the PIP (for progressive integer programming) method and providing some details for its implementation and tuning possibilities, we demonstrate, via an extensive set of computational experiments, the superior performance of the progressive approach over the direct solution of the full-integer formulation of the LPCCs in obtaining high-quality solutions. It is also shown that the solution obtained at the termination of the PIP method is a local minimizer of the LPCC, a property that cannot be claimed by any known non-enumerative method for solving this nonconvex program. In all the experiments, the PIP method is initiated at a feasible solution of the LPCC obtained from a nonlinear programming solver, and with high likelihood, can successfully improve it. Thus, the PIP method can improve a stationary solution of an indefinite QP, something that is not likely to be achievable by a nonlinear programming method. Finally, some analysis is presented that provides a better understanding of the roles of the LPCC suboptimal solutions in the local optimality of the indefinite QP. This local aspect of the connection between a QP and its LPCC formulation has seemingly not been addressed in the literature.<\/jats:p>","DOI":"10.1007\/s12532-025-00290-2","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T06:07:49Z","timestamp":1758002869000},"page":"135-182","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improving the solution of indefinite quadratic programs and linear programs with complementarity constraints by a progressive MIP method"],"prefix":"10.1007","volume":"18","author":[{"given":"Xinyao","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Shaoning","family":"Han","sequence":"additional","affiliation":[]},{"given":"Jong-Shi","family":"Pang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"290_CR1","first-page":"34","volume":"80","author":"KM Anstreicher","year":"2001","unstructured":"Anstreicher, K.M., Brixus, N.W.: A new bound for the quadratic assignment problem based on convex quadratic programming. Math. Program. 80, 34\u2013357 (2001)","journal-title":"Math. Program."},{"key":"290_CR2","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1080\/10556780108805828","volume":"16","author":"KM Anstreicher","year":"2001","unstructured":"Anstreicher, K.M., Brixus, N.W.: Solving quadratic assignment problems using convex quadratic programming relaxations. Optimization Methods and Software 16, 49\u201368 (2001)","journal-title":"Optimization Methods and Software"},{"issue":"3","key":"290_CR3","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s101070100255","volume":"91","author":"KM Anstreicher","year":"2002","unstructured":"Anstreicher, K.M., Brixus, N.W., Goux, J.P., Linderoth, J.: Solving large quadratic assignment problems on computational grids. Math. Program. 91(3), 563\u2013588 (2002)","journal-title":"Math. Program."},{"key":"290_CR4","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/s10957-007-9263-4","volume":"134","author":"C Audel","year":"2007","unstructured":"Audel, C., Savard, S., Zghal, W.: New branch-and-cut algorithm for bilevel linear programming. J. Optim. Theory Appl. 134, 353\u2013370 (2007)","journal-title":"J. Optim. Theory Appl."},{"issue":"11","key":"290_CR5","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1057\/jors.1982.210","volume":"33","author":"MS Bazaraa","year":"1982","unstructured":"Bazaraa, M.S., Sherali, H.D.: On the use of exact and heuristic cutting plane methods for the quadratic assignment problem. J. Oper. Res. Soc. 33(11), 991\u20131003 (1982)","journal-title":"J. Oper. Res. Soc."},{"key":"290_CR6","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1023\/A:1008369322970","volume":"13","author":"IM Bomze","year":"1998","unstructured":"Bomze, I.M.: On standard quadratic optimization problems. J. Global Optim. 13, 369\u2013387 (1998)","journal-title":"J. Global Optim."},{"key":"290_CR7","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1023\/A:1020209017701","volume":"24","author":"IM Bomze","year":"2002","unstructured":"Bomze, I.M., De Klerk, E.: Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. J. Global Optim. 24, 163\u2013185 (2002)","journal-title":"J. Global Optim."},{"key":"290_CR8","unstructured":"Bruengger, J., Clausen, J., Marzetta, A., Perregaard, M.: Joining forces in solving large-scale quadratic assignment problems in parallel. DIKU Technical Report, University of Copenhagen (1996)"},{"key":"290_CR9","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1023\/A:1008293323270","volume":"10","author":"RE Burkard","year":"1997","unstructured":"Burkard, R.E., Karisch, S.E., Rendl, F.: QAPLIB - A quadratic assignment problem library. J. Global Optim. 10, 391\u2013403 (1997)","journal-title":"J. Global Optim."},{"key":"290_CR10","doi-asserted-by":"publisher","unstructured":"Burkard, R.E., Offermann, J.: Entwurf von Schreibmaschinentastaturen mittels quadratischer Zuordnungsprobleme. Z. Oper. Res. 21, B121\u2013B132 (1977). https:\/\/doi.org\/10.1007\/BF01918175","DOI":"10.1007\/BF01918175"},{"issue":"4","key":"290_CR11","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1137\/S1052623497325107","volume":"9","author":"RH Byrd","year":"1999","unstructured":"Byrd, R.H., Hribar, M.E., Nocedal, J.M.: An interior-point algorithm for large-scale nonlinear programming. SIAM J. Optim. 9(4), 877\u2013900 (1999)","journal-title":"SIAM J. Optim."},{"key":"290_CR12","doi-asserted-by":"crossref","unstructured":"Byrd, R.H., Nocedal, J., Waltz, R.A.: KNITRO: An integrated package for nonlinear optimization. Large-Scale Nonlinear Optimization, 35\u201359 (2006). Springer","DOI":"10.1007\/0-387-30065-1_4"},{"issue":"1","key":"290_CR13","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s12532-011-0033-9","volume":"4","author":"J Chen","year":"2012","unstructured":"Chen, J., Burer, S.: Globally solving non-convex quadratic programming problems via completely positive programming. Math. Program. Comput. 4(1), 33\u201352 (2012)","journal-title":"Math. Program. Comput."},{"key":"290_CR14","doi-asserted-by":"crossref","unstructured":"Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. SIAM Classics in Applied Mathematics. Volume 60 (Philadelphia 2009). [Originally published by Academic Press, Boston (1992)]","DOI":"10.1137\/1.9780898719000"},{"key":"290_CR15","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s10957-020-01716-8","volume":"186","author":"Y Cui","year":"2020","unstructured":"Cui, Y., Chang, T.H., Hong, M., Pang, J.S.: A study of piecewise-linear quadratic programs. J. Optim. Theory Appl. 186, 523\u2013553 (2020)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"290_CR16","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1109\/99.714603","volume":"5","author":"J Czyzyk","year":"1998","unstructured":"Czyzyk, J., Mesnier, M.P., Mor\u00e9, J.J.: The NEOS Server. IEEE Journal on Computational Science and Engineering 5(3), 68\u201375 (1998)","journal-title":"IEEE Journal on Computational Science and Engineering"},{"key":"290_CR17","doi-asserted-by":"crossref","unstructured":"Dolan, E. D.: The NEOS Server 4.0 Administrative Guide. Mathematics and Computer Science Division, Argonne National Laboratory, Technical Memorandum ANL\/MCS-TM-250 (2001)","DOI":"10.2172\/822567"},{"key":"290_CR18","unstructured":"Eschermann, B., Wunderlich, H.J.: Optimized synthesis of self-testable finite state machines. In 20th International Symposium on Fault-Tolerant Computing (FFTCS 20), Newcastle upon Tyne, 26-28th June, (1990)"},{"key":"290_CR19","doi-asserted-by":"crossref","unstructured":"Facchinei, F., Pang, J.S.: Finite-dimensional variational inequalities and complementarity problems. Volumes\u00a01 and 2. Operations Research and Financial Engineering. Springer, New York (2003)","DOI":"10.1007\/b97543"},{"issue":"1","key":"290_CR20","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1080\/10556788.2010.512956","volume":"27","author":"H Fang","year":"2020","unstructured":"Fang, H., Leyffer, S., Munson, T.S.: A pivoting algorithm for linear programming with complementarity constraints. Optimization Methods and Software 27(1), 89\u2013114 (2020)","journal-title":"Optimization Methods and Software"},{"key":"290_CR21","doi-asserted-by":"crossref","unstructured":"Fang, Y., Liu, J., Pang, J.S.: Treatment learning with Gini constraints by Heaviside composite optimization and a progressive method. Computational Optimization and Applications. 1\u201343 (2025)","DOI":"10.1007\/s10589-025-00706-8"},{"issue":"1","key":"290_CR22","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1080\/10556780410001654241","volume":"19","author":"R Fletcher","year":"2004","unstructured":"Fletcher, R., Leyffer, S.: Solving mathematical program with complementarity constraints as nonlinear programs. Optimization Methods and Software 19(1), 15\u201340 (2004)","journal-title":"Optimization Methods and Software"},{"issue":"2","key":"290_CR23","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s101070100244","volume":"91","author":"R Fletcher","year":"2002","unstructured":"Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91(2), 239\u2013269 (2002)","journal-title":"Math. Program."},{"key":"290_CR24","doi-asserted-by":"crossref","unstructured":"Giannessi, F., Tomasin, E.: Nonconvex quadratic programs, linear complementarity problems, and integer linear programs. In: Conti, R., Ruberti, A. (eds.) Fifth Conference on Optimization Techniques (Rome 1973), Part I. Lecture Notes in Computer Science 3 (Springer, Berlin 1973) pp. 437\u2013449","DOI":"10.1007\/3-540-06583-0_43"},{"key":"290_CR25","unstructured":"Gropp, W., Mor\u00e9, J. J.: Optimization Environments and the NEOS Server. In: Buhman, M. D., Iserles, A. (eds.) Approximation Theory and Optimization. Cambridge University Press pp. 167\u2013182 (1997)"},{"key":"290_CR26","unstructured":"gurobi Optimization, LLC. GUROBI Optimizer Reference Manual. (2023). https:\/\/www.gurobi.com"},{"key":"290_CR27","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10107-010-0426-y","volume":"133","author":"J Hu","year":"2012","unstructured":"Hu, J., Mitchell, J.E., Pang, J.S.: An LPCC approach to nonconvex quadratic programs. Mathematical Programming, Series A 133, 243\u2013277 (2012)","journal-title":"Mathematical Programming, Series A"},{"issue":"1","key":"290_CR28","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1137\/07068463x","volume":"19","author":"J Hu","year":"2008","unstructured":"Hu, J., Mitchell, J.E., Pang, J.S., Bennett, K., Kunapuli, G.: On the global solution of linear programs with linear complementarity constraints. SIAM J. Optim. 19(1), 445\u2013471 (2008)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"290_CR29","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10898-010-9644-3","volume":"53","author":"J Hu","year":"2012","unstructured":"Hu, J., Mitchell, J.E., Pang, J.S., Yu, B.: On linear programs with linear complementarity constraints. J. Global Optim. 53(1), 29\u201351 (2012)","journal-title":"J. Global Optim."},{"key":"290_CR30","unstructured":"Jara-Moroni, F.J.: Methods for Linear Programs with Complementarity Constraints. Ph.D. dissertation, Department of Industrial Engineering and Management Science. Northwestern University (September 2018)"},{"key":"290_CR31","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s10898-020-00905-z","volume":"77","author":"FJ Jara-Moroni","year":"2020","unstructured":"Jara-Moroni, F.J., Mitchell, J.E., Pang, J.S., W\u00e4chter, A.: An enhanced logical Benders approach for solving linear programs with complementarity constraints. J. Global Optim. 77, 687\u2013714 (2020)","journal-title":"J. Global Optim."},{"key":"290_CR32","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10107-017-1208-6","volume":"169","author":"F Jara-Moroni","year":"2018","unstructured":"Jara-Moroni, F., Pang, J.S., W\u00e4chter, A.: A study of the difference-of-convex approach for solving linear programs with complementarity constraints. Math. Program. 169, 221\u2013254 (2018)","journal-title":"Math. Program."},{"issue":"1","key":"290_CR33","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10898-006-9001-8","volume":"36","author":"JJ J\u00fadice","year":"2006","unstructured":"J\u00fadice, J.J., Sherali, H.D., Ribeiro, I.M., Faustino, A.M.: A complementarity-based partitioning and disjunctive cut algorithm for mathematical programming problems with equilibrium constraints. J. Global Optim. 36(1), 89\u2013114 (2006)","journal-title":"J. Global Optim."},{"issue":"1","key":"290_CR34","doi-asserted-by":"publisher","first-page":"53","DOI":"10.2307\/1907742","volume":"25","author":"TC Koopmans","year":"1957","unstructured":"Koopmans, T.C., Beckmann, M.: Assignment Problems and the Location of Economic Activities. Econometrica 25(1), 53\u201376 (1957)","journal-title":"Econometrica"},{"key":"290_CR35","unstructured":"Lee, G.M., Tam, N.N., Yen, N.D.: Quadratic Programming and Affine Variational Inequalities: A Qualitative Study. Springer (New York 2005)"},{"key":"290_CR36","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical Programs With Equilibrium Constraints","author":"ZQ Luo","year":"1996","unstructured":"Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical Programs With Equilibrium Constraints. Cambridge University Press, Cambridge, England (1996)"},{"key":"290_CR37","doi-asserted-by":"publisher","first-page":"533","DOI":"10.4153\/CJM-1965-053-6","volume":"17","author":"TS Motzkin","year":"1965","unstructured":"Motzkin, T.S., Straus, E.G.: Maxima for graphs and a new proof of a theorem of Tur\u00edn. Can. J. Math. 17, 533\u2013540 (1965)","journal-title":"Can. J. Math."},{"issue":"4","key":"290_CR38","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1023\/A:1008315627883","volume":"14","author":"I Nowak","year":"1999","unstructured":"Nowak, I.: A new semidefinite programming bound for indefinite quadratic forms over a simplex. J. Global Optim. 14(4), 357\u2013364 (1999)","journal-title":"J. Global Optim."},{"key":"290_CR39","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1287\/opre.16.1.150","volume":"16","author":"CE Nugent","year":"1968","unstructured":"Nugent, C.E., Vollmann, T.E., Ruml, J.: An experimental comparison of techniques for the assignment of facilities to locations. Oper. Res. 16, 150\u2013173 (1968)","journal-title":"Oper. Res."},{"key":"290_CR40","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s10107-010-0395-1","volume":"125","author":"JS Pang","year":"2010","unstructured":"Pang, J.S.: Three modeling paradigms in mathematical programming. Mathematical Programming, Series B 125, 297\u2013323 (2010)","journal-title":"Mathematical Programming, Series B"},{"key":"290_CR41","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1023\/A:1008656806889","volume":"13","author":"JS Pang","year":"1999","unstructured":"Pang, J.S., Fukushima, M.: Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints. Comput. Optim. Appl. 13, 111\u2013136 (1999)","journal-title":"Comput. Optim. Appl."},{"key":"290_CR42","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF00120662","volume":"1","author":"PM Pardalos","year":"1991","unstructured":"Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP-hard. J. Global Optim. 1, 15\u201322 (1991)","journal-title":"J. Global Optim."},{"key":"290_CR43","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, 201\u2013205 (1996)","journal-title":"J. Global Optim."},{"issue":"13","key":"290_CR44","doi-asserted-by":"publisher","first-page":"2439","DOI":"10.1016\/j.dam.2007.09.020","volume":"156","author":"A Scozzari","year":"2008","unstructured":"Scozzari, A., Tardella, F.: A clique algorithm for standard quadratic programming. Discret. Appl. Math. 156(13), 2439\u20132448 (2008)","journal-title":"Discret. Appl. Math."},{"key":"290_CR45","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/S0167-8191(05)80147-4","volume":"17","author":"ED Taillard","year":"1991","unstructured":"Taillard, E.D.: Robust tabu search for the quadratic assignment problem. Parallel Comput. 17, 443\u2013455 (1991)","journal-title":"Parallel Comput."},{"key":"290_CR46","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0966-8349(95)00008-6","volume":"3","author":"ED Taillard","year":"1995","unstructured":"Taillard, E.D.: Comparison of iterative searches for the quadratic assignment problem. Locat. Sci. 3, 87\u2013105 (1995)","journal-title":"Locat. Sci."},{"key":"290_CR47","unstructured":"Talbi, E.G., Hafidi, Z., Geib, J.-M.: Parallel adaptive tabu search for large optimization ]problems. Research report, LIFL, University of Lille (March 1997)"},{"key":"290_CR48","unstructured":"Thonemann, U.\u00a0W., B\u00f6lte, A.: An improved simulated annealing algorithm for the quadratic assignment problem. Working Paper, School of Business, Department of Production and Operations Research, University of Paderborn, Germany (1994)"},{"key":"290_CR49","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0020-0190(90)90100-C","volume":"36","author":"SA Vavasis","year":"1990","unstructured":"Vavasis, S.A.: Quadratic programming is in NP. Inf. Process. Lett. 36, 73\u201377 (1990)","journal-title":"Inf. Process. Lett."},{"key":"290_CR50","unstructured":"W\u00e4chter, A., Biegler, L.T.: Ipopt documentation. https:\/\/coin-or.github.io\/Ipopt"},{"issue":"1","key":"290_CR51","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2006)","journal-title":"Math. Program."},{"issue":"1","key":"290_CR52","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1287\/ijoc.2018.0883","volume":"32","author":"W Xia","year":"2020","unstructured":"Xia, W., Vera, J.C., Zuluaga, L.F.: Globally solving nonconvex quadratic programs via linear integer programming techniques. INFORMS J. Comput. 32(1), 40\u201356 (2020)","journal-title":"INFORMS J. Comput."},{"issue":"2","key":"290_CR53","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s12532-018-0149-2","volume":"11","author":"B Yu","year":"2019","unstructured":"Yu, B., Mitchell, J.C., Pang, J.S.: Solving linear programs with complementarity constraints using branch-and-cut. Math. Program. Comput. 11(2), 267\u2013310 (2019)","journal-title":"Math. Program. Comput."},{"key":"290_CR54","unstructured":"Zhang, X., Han, S., Pang, J.S.: Code for Improving the Solution of Indefinite Quadratic Programs and Linear Programs with Complementarity Constraints by a Progressive MIP Method https:\/\/doi.org\/10.5281\/zenodo.16467564"}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-025-00290-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12532-025-00290-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-025-00290-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T12:02:15Z","timestamp":1772625735000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12532-025-00290-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,16]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["290"],"URL":"https:\/\/doi.org\/10.1007\/s12532-025-00290-2","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,16]]},"assertion":[{"value":"24 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2025","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 that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}