{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T09:50:57Z","timestamp":1775037057849,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:00:00Z","timestamp":1759190400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:00:00Z","timestamp":1759190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100010324","name":"Secretar\u00eda General de Ciencia y T\u00e9cnica, Universidad Nacional del Nordeste","doi-asserted-by":"publisher","award":["19F010"],"award-info":[{"award-number":["19F010"]}],"id":[{"id":"10.13039\/501100010324","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006668","name":"Fondo para la Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"publisher","award":["PICT-2021-GRF-TI-00188"],"award-info":[{"award-number":["PICT-2021-GRF-TI-00188"]}],"id":[{"id":"10.13039\/501100006668","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006668","name":"Fondo para la Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"publisher","award":["PICT-2019-2019-04569"],"award-info":[{"award-number":["PICT-2019-2019-04569"]}],"id":[{"id":"10.13039\/501100006668","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad Nacional de C\u00f3rdoba","award":["33620230100671CB"],"award-info":[{"award-number":["33620230100671CB"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s10957-025-02847-6","type":"journal-article","created":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T13:11:42Z","timestamp":1759237902000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancing Sharp Augmented Lagrangian Methods with Smoothing Techniques for Nonlinear Programming"],"prefix":"10.1007","volume":"208","author":[{"given":"Jos\u00e9 Luis","family":"Romero","sequence":"first","affiliation":[]},{"given":"Dami\u00e1n","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5186-5061","authenticated-orcid":false,"given":"Germ\u00e1n Ariel","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,30]]},"reference":[{"issue":"1","key":"2847_CR1","first-page":"5","volume":"111","author":"R Andreani","year":"2008","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111(1), 5\u201332 (2008)","journal-title":"Math. Program."},{"issue":"4","key":"2847_CR2","doi-asserted-by":"publisher","first-page":"1286","DOI":"10.1137\/060654797","volume":"18","author":"R Andreani","year":"2008","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18(4), 1286\u20131309 (2008)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2847_CR3","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. Comput. Optim. Appl. 45(2), 209\u2013236 (2010)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"2847_CR4","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1080\/02331930500100270","volume":"54","author":"M Andretta","year":"2005","unstructured":"Andretta, M., Birgin, E.G., Mart\u00ednez, J.M.: Practical active-set Euclidean trust-region method with spectral projected gradients for bound-constrained minimization. Optimization 54(3), 305\u2013325 (2005)","journal-title":"Optimization"},{"issue":"3","key":"2847_CR5","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1080\/10556788.2018.1496431","volume":"34","author":"AM Bagirov","year":"2019","unstructured":"Bagirov, A.M., Ozturk, G., Kasimbeyli, R.: A sharp augmented Lagrangian-based method in constrained non-convex optimization. Optimization Methods Softw. 34(3), 462\u2013488 (2019)","journal-title":"Optimization Methods Softw."},{"key":"2847_CR6","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, Computer Science and Applied Mathematics (1982)"},{"issue":"1","key":"2847_CR7","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10589-005-1066-7","volume":"31","author":"EG Birgin","year":"2005","unstructured":"Birgin, E.G., Castillo, R.A., Mart\u00ednez, J.M.: Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl. 31(1), 31\u201355 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"2847_CR8","doi-asserted-by":"crossref","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: A box\u2013constrained optimization algorithm with negative curvature directions and spectral projected gradients. In Topics in Numerical Analysis: With Special Emphasis on Nonlinear Problems, pp. 49\u201360. Springer (2001)","DOI":"10.1007\/978-3-7091-6217-0_5"},{"key":"2847_CR9","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"EG Birgin","year":"2002","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 23, 101\u2013125 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"2847_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10589-007-9050-z","volume":"39","author":"EG Birgin","year":"2008","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Structured minimal-memory inexact quasi-newton method and secant preconditioners for augmented Lagrangian optimization. Comput. Optim. Appl. 39, 1\u201316 (2008)","journal-title":"Comput. Optim. Appl."},{"key":"2847_CR11","doi-asserted-by":"crossref","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Practical Augmented Lagrangian Methods for Constrained Optimization, SIAM (2014)","DOI":"10.1137\/1.9781611973365"},{"issue":"4","key":"2847_CR12","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"EG Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10(4), 1196\u20131211 (2000)","journal-title":"SIAM J. Optim."},{"key":"2847_CR13","unstructured":"Bonnans, J.F., Gilbert, J.C., Lemar\u00e9chal, C., and Sagastiz\u00e1bal, C.A.: Numerical Optimization: Theoretical and Practical Aspects, Springer Science & Business Media (2006)"},{"key":"2847_CR14","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s10898-005-3270-5","volume":"34","author":"RS Burachik","year":"2006","unstructured":"Burachik, R.S., Gasimov, R.N., Ismayilova, N.A., Kaya, C.Y.: On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian. J. Global Optim. 34, 55\u201378 (2006)","journal-title":"J. Global Optim."},{"key":"2847_CR15","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s10898-009-9429-8","volume":"46","author":"RS Burachik","year":"2010","unstructured":"Burachik, R.S., Iusem, A.N., Melo, J.G.: A primal dual modified subgradient algorithm with sharp Lagrangian. J. Global Optim. 46, 347\u2013361 (2010)","journal-title":"J. Global Optim."},{"issue":"3","key":"2847_CR16","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1137\/S1052623493251463","volume":"6","author":"AR Conn","year":"1996","unstructured":"Conn, A.R., Gould, N.I.M., Sartenaer, A., Toint, P.L.: Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints. SIAM J. Optim. 6(3), 674\u2013703 (1996)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2847_CR17","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1137\/0728030","volume":"28","author":"AR Conn","year":"1991","unstructured":"Conn, A.R., Gould, N.I.M., Toint, P.: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28(2), 545\u2013572 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"2847_CR18","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Gould, N.I.M., Toint, Ph.L.: LANCELOT: a Fortran Package for Large\u2013Scale Nonlinear Optimization (Release A), volume 17 of Springer Series in Computational Mathematics, Springer\u2013Verlag, Berlin (1992)","DOI":"10.1007\/978-3-662-12211-2"},{"issue":"1","key":"2847_CR19","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1080\/02331934.2020.1804567","volume":"71","author":"D Fern\u00e1ndez","year":"2022","unstructured":"Fern\u00e1ndez, D.: Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions. Optimization 71(1), 97\u2013115 (2022)","journal-title":"Optimization"},{"issue":"2","key":"2847_CR20","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1137\/10081085X","volume":"22","author":"D Fern\u00e1ndez","year":"2012","unstructured":"Fern\u00e1ndez, D., Solodov, M.V.: Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition. SIAM J. Optim. 22(2), 384\u2013407 (2012)","journal-title":"SIAM J. Optim."},{"key":"2847_CR21","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1023\/A:1020261001771","volume":"24","author":"RN Gasimov","year":"2002","unstructured":"Gasimov, R.N.: Augmented Lagrangian duality and nondifferentiable optimization methods in nonconvex programming. J. Global Optim. 24, 187\u2013203 (2002)","journal-title":"J. Global Optim."},{"key":"2847_CR22","unstructured":"Gon\u00e7alves de Melo, J.D.: On general augmented Lagrangians and a modified subgradient algorithm. PhD Thesis, IMPA, Rio de Janeiro, (2009)"},{"key":"2847_CR23","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1007\/s10589-014-9687-3","volume":"60","author":"NIM Gould","year":"2015","unstructured":"Gould, N.I.M., Orban, D., Toint, P.L.: Cutest: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Comput. Optim. Appl. 60, 545\u2013557 (2015)","journal-title":"Comput. Optim. Appl."},{"key":"2847_CR24","unstructured":"Hedar, A.R.: Global optimization test problems. http:\/\/www-optima.amp.i.kyoto-u.ac.jp\/member\/student\/hedar\/Hedar files\/TestGO.htm"},{"issue":"5","key":"2847_CR25","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4(5), 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"2847_CR26","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/BF00934594","volume":"30","author":"W Hock","year":"1980","unstructured":"Hock, W., Schittkowski, K.: Test examples for nonlinear programming codes. J. Optim. Theory Appl. 30, 127\u2013129 (1980)","journal-title":"J. Optim. Theory Appl."},{"issue":"5","key":"2847_CR27","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1080\/02331930902928419","volume":"58","author":"R Kasimbeyli","year":"2009","unstructured":"Kasimbeyli, R., Ustun, O., Rubinov, A.M.: The modified subgradient algorithm based on feasible values. Optimization 58(5), 535\u2013560 (2009)","journal-title":"Optimization"},{"key":"2847_CR28","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Newyork (2006)"},{"issue":"1","key":"2847_CR29","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1287\/moor.27.1.170.331","volume":"27","author":"T Pennanen","year":"2002","unstructured":"Pennanen, T.: Local convergence of the proximal point algorithm and multiplier methods without monotonicity. Math. Oper. Res. 27(1), 170\u2013191 (2002)","journal-title":"Math. Oper. Res."},{"key":"2847_CR30","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. Optimization, 283\u2013298 (1969)"},{"issue":"2","key":"2847_CR31","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented lagrange multiplier functions and duality in nonconvex programming. SIAM Journal on Control 12(2), 268\u2013285 (1974)","journal-title":"SIAM Journal on Control"},{"key":"2847_CR32","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, vol. 317. Springer Science & Business Media, Newyork (2009)"},{"issue":"39","key":"2847_CR33","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1080\/14786440409463107","volume":"7","author":"JJ Thomson","year":"1904","unstructured":"Thomson, J.J.: On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure. Phil. Mag. 7(39), 237\u2013265 (1904)","journal-title":"Phil. Mag."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02847-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-025-02847-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02847-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T07:22:16Z","timestamp":1775028136000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-025-02847-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,30]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["2847"],"URL":"https:\/\/doi.org\/10.1007\/s10957-025-02847-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,30]]},"assertion":[{"value":"26 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 September 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"23"}}