{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:00:29Z","timestamp":1760162429635,"version":"3.41.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["309136\/2021-0","407147\/2023-3","307987\/2023-0","403418\/2023-2"],"award-info":[{"award-number":["309136\/2021-0","407147\/2023-3","307987\/2023-0","403418\/2023-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2024\/12967-8"],"award-info":[{"award-number":["2024\/12967-8"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s10957-025-02705-5","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T04:29:01Z","timestamp":1747974541000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Practical Second-Order Optimality Condition for Cardinality-Constrained Problems with Application to an Augmented Lagrangian Method"],"prefix":"10.1007","volume":"206","author":[{"given":"Jean C. A.","family":"Medeiros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ademir A.","family":"Ribeiro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mael","family":"Sachine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9224-9051","authenticated-orcid":false,"given":"Leonardo D.","family":"Secchin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,23]]},"reference":[{"issue":"2","key":"2705_CR1","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s10589-009-9240-y","volume":"45","author":"R Andreani","year":"2010","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Second-order negative-curvature methods for box-constrained and general constrained optimization. Computational Optimization and Applications 45(2), 209\u2013236 (2010). https:\/\/doi.org\/10.1007\/s10589-009-9240-y","journal-title":"Computational Optimization and Applications"},{"issue":"4","key":"2705_CR2","doi-asserted-by":"publisher","first-page":"1286","DOI":"10.1137\/060654797","volume":"18","author":"R Andreani","year":"2007","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM Journal on Optimization 18(4), 1286\u20131309 (2007). https:\/\/doi.org\/10.1137\/060654797","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"2705_CR3","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10957-010-9671-8","volume":"146","author":"R Andreani","year":"2010","unstructured":"Andreani, R., Echag\u00fce, C.E., Schuverdt, M.L.: Constant-rank condition and second-order constraint qualification. Journal of Optimization Theory and Applications 146(2), 255\u2013266 (2010). https:\/\/doi.org\/10.1007\/s10957-010-9671-8","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"4","key":"2705_CR4","doi-asserted-by":"publisher","first-page":"1902","DOI":"10.1093\/imanum\/drw064","volume":"37","author":"R Andreani","year":"2017","unstructured":"Andreani, R., Haeser, G., Ramos, A., Silva, P.J.S.: A second-order sequential optimality condition associated to the convergence of optimization algorithms. IMA Journal of Numerical Analysis 37(4), 1902\u20131929 (2017). https:\/\/doi.org\/10.1093\/imanum\/drw064","journal-title":"IMA Journal of Numerical Analysis"},{"issue":"1","key":"2705_CR5","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10107-011-0456-0","volume":"135","author":"R Andreani","year":"2012","unstructured":"Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: A relaxed constant positive linear dependence constraint qualification and applications. Mathematical Programming 135(1), 255\u2013273 (2012). https:\/\/doi.org\/10.1007\/s10107-011-0456-0","journal-title":"Mathematical Programming"},{"issue":"4","key":"2705_CR6","doi-asserted-by":"publisher","first-page":"3201","DOI":"10.1137\/18M121040X","volume":"29","author":"R Andreani","year":"2019","unstructured":"Andreani, R., Haeser, G., Secchin, L.D., Silva, P.J.S.: New sequential optimality conditions for mathematical programs with complementarity constraints and algorithmic consequences. SIAM Journal on Optimization 29(4), 3201\u20133230 (2019). https:\/\/doi.org\/10.1137\/18M121040X","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"2705_CR7","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1137\/15M1008488","volume":"26","author":"R Andreani","year":"2016","unstructured":"Andreani, R., Mart\u00ednez, J.M., Ramos, A., Silva, P.J.S.: A cone-continuity constraint qualification and algorithmic consequences. SIAM Journal on Optimization 26(1), 96\u2013110 (2016). https:\/\/doi.org\/10.1137\/15M1008488","journal-title":"SIAM Journal on Optimization"},{"issue":"5\u20136","key":"2705_CR8","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1080\/02331930701618617","volume":"56","author":"R Andreani","year":"2007","unstructured":"Andreani, R., Mart\u00ednez, J.M., Schuverdt, M.L.: On second-order optimality conditions for nonlinear programming. Optimization 56(5\u20136), 529\u2013542 (2007). https:\/\/doi.org\/10.1080\/02331930701618617","journal-title":"Optimization"},{"issue":"6","key":"2705_CR9","doi-asserted-by":"publisher","first-page":"3533","DOI":"10.1137\/090777189","volume":"20","author":"R Andreani","year":"2010","unstructured":"Andreani, R., Mart\u00ednez, J.M., Svaiter, B.F.: A new sequential optimality condition for constrained optimization and algorithmic consequences. SIAM Journal on Optimization 20(6), 3533\u20133554 (2010). https:\/\/doi.org\/10.1137\/090777189","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"2705_CR10","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1093\/imanum\/drab021","volume":"42","author":"R Andreani","year":"2021","unstructured":"Andreani, R., Ramos, A., Ribeiro, A.A., Secchin, L.D., Velazco, A.R.: On the convergence of augmented Lagrangian strategies for nonlinear programming. IMA Journal of Numerical Analysis 42(2), 1735\u20131765 (2021). https:\/\/doi.org\/10.1093\/imanum\/drab021","journal-title":"IMA Journal of Numerical Analysis"},{"key":"2705_CR11","doi-asserted-by":"publisher","unstructured":"Andreani, R., Secchin, L.D.: A note on the convergence of an augmented Lagrangian algorithm to second-order stationary points. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, vol.\u00a06. Sociedade Brasileira de Matem\u00e1tica Aplicada e Computacional (2018). https:\/\/doi.org\/10.5540\/03.2018.006.01.0303","DOI":"10.5540\/03.2018.006.01.0303"},{"issue":"3","key":"2705_CR12","doi-asserted-by":"publisher","first-page":"2574","DOI":"10.1137\/17M1125698","volume":"28","author":"R Andreani","year":"2018","unstructured":"Andreani, R., Secchin, L.D., Silva, P.J.S.: Convergence properties of a second order augmented Lagrangian method for mathematical programs with complementarity constraints. SIAM Journal on Optimization 28(3), 2574\u20132600 (2018). https:\/\/doi.org\/10.1137\/17M1125698","journal-title":"SIAM Journal on Optimization"},{"key":"2705_CR13","doi-asserted-by":"publisher","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Practical Augmented Lagrangian Methods for Constrained Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA (2014). https:\/\/doi.org\/10.1137\/1.9781611973365","DOI":"10.1137\/1.9781611973365"},{"issue":"2","key":"2705_CR14","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s10589-018-9985-2","volume":"70","author":"M Branda","year":"2018","unstructured":"Branda, M., Bucher, M., \u010cervinka, M., Schwartz, A.: Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization. Computational Optimization and Applications 70(2), 503\u2013530 (2018). https:\/\/doi.org\/10.1007\/s10589-018-9985-2","journal-title":"Computational Optimization and Applications"},{"issue":"2","key":"2705_CR15","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s10957-018-1320-7","volume":"178","author":"M Bucher","year":"2018","unstructured":"Bucher, M., Schwartz, A.: Second-order optimality conditions and improved convergence results for regularization methods for cardinality-constrained optimization problems. Journal of Optimization Theory and Applications 178(2), 383\u2013410 (2018). https:\/\/doi.org\/10.1007\/s10957-018-1320-7","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"2705_CR16","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1137\/140978077","volume":"26","author":"OP Burdakov","year":"2016","unstructured":"Burdakov, O.P., Kanzow, C., Schwartz, A.: Mathematical programs with cardinality constraints: reformulation by complementarity-type conditions and a regularization method. SIAM Journal on Optimization 26(1), 397\u2013425 (2016). https:\/\/doi.org\/10.1137\/140978077","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"2705_CR17","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/s10107-016-0986-6","volume":"160","author":"M \u010cervinka","year":"2016","unstructured":"\u010cervinka, M., Kanzow, C., Schwartz, A.: Constraint qualifications and optimality conditions for optimization problems with cardinality constraints. Mathematical Programming 160(1), 353\u2013377 (2016). https:\/\/doi.org\/10.1007\/s10107-016-0986-6","journal-title":"Mathematical Programming"},{"issue":"3","key":"2705_CR18","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10957-004-1176-x","volume":"124","author":"ML Flegel","year":"2005","unstructured":"Flegel, M.L., Kanzow, C.: Abadie-type constraint qualification for mathematical programs with equilibrium constraints. Journal of Optimization Theory and Applications 124(3), 595\u2013614 (2005). https:\/\/doi.org\/10.1007\/s10957-004-1176-x","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"2","key":"2705_CR19","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s101070050066","volume":"85","author":"NIM Gould","year":"1999","unstructured":"Gould, N.I.M., Toint, P.L.: A note on the convergence of barrier algorithms to second-order necessary points. Mathematical Programming 85(2), 433\u2013438 (1999). https:\/\/doi.org\/10.1007\/s101070050066","journal-title":"Mathematical Programming"},{"key":"2705_CR20","doi-asserted-by":"publisher","unstructured":"Janin, R.: Directional derivative of the marginal function in nonlinear programming. In: A.V. Fiacco (ed.) Sensitivity, Stability and Parametric Analysis, Mathematical Programming Studies, vol.\u00a021, pp. 110\u2013126. Springer Berlin Heidelberg, Berlin, Heidelberg (1984). https:\/\/doi.org\/10.1007\/BFb0121214","DOI":"10.1007\/BFb0121214"},{"issue":"3","key":"2705_CR21","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1007\/s10957-021-01854-7","volume":"189","author":"C Kanzow","year":"2021","unstructured":"Kanzow, C., Raharja, A.B., Schwartz, A.: An augmented Lagrangian method for cardinality-constrained optimization problems. Journal of Optimization Theory and Applications 189(3), 793\u2013813 (2021). https:\/\/doi.org\/10.1007\/s10957-021-01854-7","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"2705_CR22","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s10589-021-00298-z","volume":"80","author":"C Kanzow","year":"2021","unstructured":"Kanzow, C., Raharja, A.B., Schwartz, A.: Sequential optimality conditions for cardinality-constrained optimization problems with applications. Computational Optimization and Applications 80(1), 185\u2013211 (2021). https:\/\/doi.org\/10.1007\/s10589-021-00298-z","journal-title":"Computational Optimization and Applications"},{"issue":"2","key":"2705_CR23","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1137\/100802487","volume":"23","author":"C Kanzow","year":"2013","unstructured":"Kanzow, C., Schwartz, A.: A new regularization method for mathematical programs with complementarity constraints with strong convergence properties. SIAM Journal on Optimization 23(2), 770\u2013798 (2013). https:\/\/doi.org\/10.1137\/100802487","journal-title":"SIAM Journal on Optimization"},{"key":"2705_CR24","doi-asserted-by":"publisher","first-page":"3451","DOI":"10.1007\/s00245-021-09752-0","volume":"84","author":"EHM Krulikovski","year":"2021","unstructured":"Krulikovski, E.H.M., Ribeiro, A.A., Sachine, M.: On the weak stationarity conditions for mathematical programs with cardinality constraints: a unified approach. Appl. Math. Optim. 84, 3451\u20133473 (2021). https:\/\/doi.org\/10.1007\/s00245-021-09752-0","journal-title":"Appl. Math. Optim."},{"issue":"1","key":"2705_CR25","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1023\/A:1004632923654","volume":"104","author":"JM Mart\u00ednez","year":"2000","unstructured":"Mart\u00ednez, J.M., Pilotta, E.A.: Inexact-restoration algorithm for constrained optimization. Journal of Optimization Theory and Applications 104(1), 135\u2013163 (2000). https:\/\/doi.org\/10.1023\/A:1004632923654","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"4","key":"2705_CR26","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1080\/02331930902971377","volume":"60","author":"L Minchenko","year":"2011","unstructured":"Minchenko, L., Stakhovski, S.: On relaxed constant rank regularity condition in mathematical programming. Optimization 60(4), 429\u2013440 (2011). https:\/\/doi.org\/10.1080\/02331930902971377","journal-title":"Optimization"},{"key":"2705_CR27","doi-asserted-by":"publisher","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, Grundlehren der mathematischen Wissenschaften, vol. 317, 1 edn. Springer-Verlag Berlin Heidelberg (1998). https:\/\/doi.org\/10.1007\/978-3-642-02431-3","DOI":"10.1007\/978-3-642-02431-3"},{"issue":"1","key":"2705_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1287\/moor.25.1.1.15213","volume":"25","author":"H Scheel","year":"2000","unstructured":"Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Mathematics of Operations Research 25(1), 1\u201322 (2000). https:\/\/doi.org\/10.1287\/moor.25.1.1.15213","journal-title":"Mathematics of Operations Research"},{"issue":"4","key":"2705_CR29","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1137\/S1052623499361233","volume":"11","author":"S Scholtes","year":"2001","unstructured":"Scholtes, S.: Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM Journal on Optimization 11(4), 918\u2013936 (2001). https:\/\/doi.org\/10.1137\/S1052623499361233","journal-title":"SIAM Journal on Optimization"},{"key":"2705_CR30","unstructured":"Tillmann, A.M., Bienstock, D., Lodi, A., Schwartz, A.: Cardinality minimization, constraints, and regularization: A survey (2021)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02705-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-025-02705-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02705-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T08:46:13Z","timestamp":1750668373000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-025-02705-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,23]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2705"],"URL":"https:\/\/doi.org\/10.1007\/s10957-025-02705-5","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2025,5,23]]},"assertion":[{"value":"19 April 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"22"}}