{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T11:06:36Z","timestamp":1777719996142,"version":"3.51.4"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T00:00:00Z","timestamp":1579824000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s10898-020-00876-1","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T16:04:20Z","timestamp":1579881860000},"page":"543-574","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Subset selection for multiple linear regression via optimization"],"prefix":"10.1007","volume":"77","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0722-7729","authenticated-orcid":false,"given":"Young Woong","family":"Park","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diego","family":"Klabjan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,1,24]]},"reference":[{"key":"876_CR1","first-page":"471","volume":"13","author":"D Bertsimas","year":"2005","unstructured":"Bertsimas, D., Weismantel, R.: Optimization over integers. Dyn. Ideas 13, 471 (2005)","journal-title":"Dyn. Ideas"},{"key":"876_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10589-007-9126-9","volume":"43","author":"D Bertsimas","year":"2009","unstructured":"Bertsimas, D., Shioda, R.: Algorithm for cardinality-constrained quadratic optimization. Comput. Optim. Appl. 43, 1\u201322 (2009)","journal-title":"Comput. Optim. Appl."},{"key":"876_CR3","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1214\/15-AOS1388","volume":"44","author":"D Bertsimas","year":"2016","unstructured":"Bertsimas, D., King, A., Mazumder, R.: Best subset selection via a modern optimization lens. Ann. Stat. 44, 813\u2013852 (2016)","journal-title":"Ann. Stat."},{"issue":"1","key":"876_CR4","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1287\/opre.2015.1436","volume":"64","author":"D Bertsimas","year":"2016","unstructured":"Bertsimas, D., King, A.: OR forum an algorithmic approach to linear regression. Oper. Res. 64(1), 2\u201316 (2016)","journal-title":"Oper. Res."},{"key":"876_CR5","first-page":"121","volume":"74","author":"D Bienstock","year":"1996","unstructured":"Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74, 121\u2013140 (1996)","journal-title":"Math. Program."},{"key":"876_CR6","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1287\/ijoc.10.2.209","volume":"10:2","author":"PS Bradley","year":"1998","unstructured":"Bradley, P.S., Mangasarian, O.L., Street, W.N.: Feature selection via mathematical programming. INFORMS J. Comput. 10:2, 209\u2013217 (1998)","journal-title":"INFORMS J. Comput."},{"key":"876_CR7","doi-asserted-by":"publisher","first-page":"2313","DOI":"10.1214\/009053606000001523","volume":"35","author":"E Candes","year":"2007","unstructured":"Candes, E., Tao, T.: The Danzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35, 2313\u20132351 (2007)","journal-title":"Ann. Stat."},{"key":"876_CR8","first-page":"1247","volume":"7:3","author":"T Chai","year":"2004","unstructured":"Chai, T., Draxler, R.R.: Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geosci. Model Dev. 7:3, 1247\u20131250 (2004)","journal-title":"Geosci. Model Dev."},{"key":"876_CR9","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1287\/mnsc.1.2.138","volume":"1","author":"A Charnes","year":"1955","unstructured":"Charnes, A., Cooper, W.W., Ferguson, R.O.: Optimal estimation of executive compensation by linear programming. Manag. Sci. 1, 138\u2013151 (1955)","journal-title":"Manag. Sci."},{"key":"876_CR10","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1007\/s10107-003-0420-8","volume":"96:3","author":"IR de Farias Jr","year":"2003","unstructured":"de Farias Jr., I.R., Nemhauser, G.L.: A polyhedral study of the cardinality constrained knapsack problem. Math. Program. 96:3, 439\u2013467 (2003)","journal-title":"Math. Program."},{"key":"876_CR11","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1080\/0094965042000223680","volume":"75:4","author":"Terry E Dielman","year":"2005","unstructured":"Dielman, Terry E.: Least absolute value regression: recent contributions. J. Stat. Comput. Simul. 75:4, 263\u2013286 (2005)","journal-title":"J. Stat. Comput. Simul."},{"key":"876_CR12","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1142\/S0219720005001004","volume":"3:2","author":"C Ding","year":"2005","unstructured":"Ding, C., Peng, H.: Minimum redundancy feature selection from microarray gene expression data. J. Bioinform. Comput. Biol. 3:2, 185\u2013205 (2005)","journal-title":"J. Bioinform. Comput. Biol."},{"key":"876_CR13","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1023\/B:COAP.0000026884.66338.df","volume":"28:2","author":"GN Fung","year":"2004","unstructured":"Fung, G.N., Mangasarian, O.L.: A feature selection Newton method for support vector machine classification. Comput. Optim. Appl. 28:2, 185\u2013202 (2004)","journal-title":"Comput. Optim. Appl."},{"key":"876_CR14","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1080\/00401706.1974.10489231","volume":"16","author":"GM Furnival","year":"1974","unstructured":"Furnival, G.M., Wilson, R.W.: Regressions by leaps and bounds. Technometrics 16, 499\u2013511 (1974)","journal-title":"Technometrics"},{"issue":"4","key":"876_CR15","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. Manag. Sci. 22(4), 455\u2013460 (1975)","journal-title":"Manag. Sci."},{"key":"876_CR16","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/173","volume-title":"Geometric Approximation Algorithms","author":"S Har-Peled","year":"2011","unstructured":"Har-Peled, S.: Geometric Approximation Algorithms. American Mathematical Society, Providence (2011)"},{"key":"876_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3462-1","volume-title":"Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis","author":"FE Harrell","year":"2001","unstructured":"Harrell, F.E.: Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. Springer, Berlin (2001)"},{"key":"876_CR18","unstructured":"Hastie, T., Tibshirani, R., Tibshirani, R.: Bestsubset: Tools for best subset selection in regression. R Package version 1.0.4 (2017). https:\/\/github.com\/ryantibs\/best-subset\/. Accessed 22 Aug 2018"},{"key":"876_CR19","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"AE Hoerl","year":"1970","unstructured":"Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55\u201367 (1970)","journal-title":"Technometrics"},{"key":"876_CR20","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10479-017-2445-z","volume":"254","author":"K Hwang","year":"2017","unstructured":"Hwang, K., Kim, D., Lee, K., Lee, C., Park, S.: Embedded variable selection method using signomial classification. Ann. Oper. Res. 254, 89\u2013109 (2017)","journal-title":"Ann. Oper. Res."},{"key":"876_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/10691898.1996.11910505","volume":"4","author":"RW Johnson","year":"1996","unstructured":"Johnson, R.W.: Fitting percentage of body fat to simple body measurements. J. Stat. Educ. 4, 1 (1996)","journal-title":"J. Stat. Educ."},{"key":"876_CR22","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s10898-008-9323-9","volume":"44","author":"H Konno","year":"2009","unstructured":"Konno, H., Yamamoto, R.: Choosing the best set of variables in regression analysis using integer programming. J. Global Optim. 44, 273\u2013282 (2009)","journal-title":"J. Global Optim."},{"key":"876_CR23","unstructured":"Lichman, M.: UCI machine learning repository (2013). http:\/\/archive.ics.uci.edu\/ml. Accessed 21 Aug 2018"},{"key":"876_CR24","unstructured":"Lumley, T.: Leaps: regression subset selection. R package version 2.9 (2009) http:\/\/CRAN.R-project.org\/package=leaps. Accessed 18 Oct 2016"},{"key":"876_CR25","doi-asserted-by":"publisher","first-page":"389","DOI":"10.2307\/2981576","volume":"147","author":"AJ Miller","year":"1984","unstructured":"Miller, A.J.: Selection of subsets of regression variables. J. R. Stat. Soc. Ser. A 147, 389\u2013425 (1984)","journal-title":"J. R. Stat. Soc. Ser. A"},{"key":"876_CR26","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035933","volume-title":"Subset Selection in Regression","author":"AJ Miller","year":"2002","unstructured":"Miller, A.J.: Subset Selection in Regression. Chapman and Hall, London (2002)"},{"key":"876_CR27","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1016\/j.ejor.2015.06.081","volume":"247","author":"R Miyashiro","year":"2015","unstructured":"Miyashiro, R., Takano, Y.: Mixed integer second-order cone programming formulations for variable selection in linear regression. Eur. J. Oper. Res. 247, 721\u2013731 (2015)","journal-title":"Eur. J. Oper. Res."},{"key":"876_CR28","doi-asserted-by":"publisher","first-page":"317","DOI":"10.2307\/1402501","volume":"50","author":"SC Narula","year":"1982","unstructured":"Narula, S.C., Wellington, J.F.: The minimum sum of absolute error regression: a state of the art survey. Int. Stat. Rev. 50, 317\u2013326 (1982)","journal-title":"Int. Stat. Rev."},{"issue":"8","key":"876_CR29","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1109\/TPAMI.2005.159","volume":"27","author":"H Peng","year":"2005","unstructured":"Peng, H., Long, F., Ding, C.: Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226\u20131238 (2005)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"876_CR30","doi-asserted-by":"publisher","first-page":"04015066","DOI":"10.1061\/(ASCE)CO.1943-7862.0001047","volume":"142","author":"MH Rafiei","year":"2015","unstructured":"Rafiei, M.H., Adeli, H.: A novel machine learning model for estimation of sale prices of real estate units. J. Constr. Eng. Manag. 142(2), 04015066 (2015)","journal-title":"J. Constr. Eng. Manag."},{"issue":"1","key":"876_CR31","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1080\/10556780903139388","volume":"25","author":"F Rinaldi","year":"2010","unstructured":"Rinaldi, F., Sciandrone, M.: Feature selection combining linear support vector machines and concave optimization. Optim. Methods Softw. 25(1), 117\u2013128 (2010)","journal-title":"Optim. Methods Softw."},{"key":"876_CR32","first-page":"493","volume":"5","author":"S Schaible","year":"2004","unstructured":"Schaible, S., Shi, J.: Recent developments in fractional programming: single-ratio and max-min case. Nonlinear Anal. Convex Anal. 5, 493\u2013506 (2004)","journal-title":"Nonlinear Anal. Convex Anal."},{"key":"876_CR33","volume-title":"Fractional Programming: Theory, Methods and Applications","author":"IM Stancu-Minasian","year":"2012","unstructured":"Stancu-Minasian, I.M.: Fractional Programming: Theory, Methods and Applications. Springer, Berlin (2012)"},{"key":"876_CR34","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1080\/01621459.1973.10481436","volume":"68","author":"EJ Schlossmacher","year":"1973","unstructured":"Schlossmacher, E.J.: An iterative technique for absolute deviations curve fitting. J. Am. Stat. Assoc. 68, 857\u2013859 (1973)","journal-title":"J. Am. Stat. Assoc."},{"key":"876_CR35","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1998","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Hoboken (1998)"},{"key":"876_CR36","unstructured":"Stodden, V.: Model selection when the number of variables exceeds the number of observations. PhD dissertation. Stanford University (2006)"},{"key":"876_CR37","volume-title":"Statistics and Data Analysis: From Elementary to Intermediate","author":"AC Tamhane","year":"1999","unstructured":"Tamhane, A.C., Dunlop, D.D.: Statistics and Data Analysis: From Elementary to Intermediate. Pearson, London (1999)"},{"key":"876_CR38","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B 58, 267\u2013288 (1996)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"876_CR39","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1080\/01621459.1959.10501506","volume":"54","author":"HM Wagner","year":"1959","unstructured":"Wagner, H.M.: Linear programming techniques for regression analysis. J. Am. Stat. Assoc. 54, 206\u2013212 (1959)","journal-title":"J. Am. Stat. Assoc."},{"key":"876_CR40","first-page":"1439","volume":"3","author":"J Western","year":"2003","unstructured":"Western, J., Elisseeff, A., Sch\u00f6lkopf, B., Tipping, M.: Use of the zero-norm with linear models and kernel methods. J. Mach. Learn. Res. 3, 1439\u20131461 (2003)","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"876_CR41","doi-asserted-by":"publisher","first-page":"79","DOI":"10.3354\/cr030079","volume":"30","author":"CJ Willmott","year":"2005","unstructured":"Willmott, C.J., Matsuura, K.: Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim. Res. 30(1), 79\u201382 (2005)","journal-title":"Clim. Res."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00876-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-020-00876-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00876-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T17:45:10Z","timestamp":1722361510000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-020-00876-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["876"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00876-1","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"assertion":[{"value":"21 September 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}