{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:41:39Z","timestamp":1740123699692,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T00:00:00Z","timestamp":1498003200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1007\/s11075-017-0366-1","type":"journal-article","created":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T02:46:10Z","timestamp":1498013170000},"page":"41-62","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Implementation of reduced gradient with bisection algorithms for non-convex optimization problem via stochastic perturbation"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9947-1408","authenticated-orcid":false,"given":"Abdelkrim El","family":"Mouatasim","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,6,21]]},"reference":[{"issue":"6","key":"366_CR1","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1080\/07408170802322986","volume":"41","author":"AN Avramidis","year":"2009","unstructured":"Avramidis, A. N., Chan, W., L\u2019Ecuyer, P.: Staffing multi-skill call centers via search methods and a performance approximation. IIE Trans. 41(6), 483\u2013497 (2009)","journal-title":"IIE Trans."},{"key":"366_CR2","first-page":"801","volume":"2","author":"AN Baushev","year":"2007","unstructured":"Baushev, A. N., Morozova, E. Y.: A multidimensional bisection method for minimizing function over simplex. Lectures Notes in Engineering and Computer Science 2, 801\u2013803 (2007)","journal-title":"Lectures Notes in Engineering and Computer Science"},{"key":"366_CR3","doi-asserted-by":"crossref","unstructured":"Bazaraa, M. S., Sherali, H. D., Shetty, C. M.: Nonlinear programming theory and application. 3rd edn. Wiley-Interscience (2006)","DOI":"10.1002\/0471787779"},{"key":"366_CR4","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1145\/356022.356025","volume":"9","author":"P Beck","year":"1983","unstructured":"Beck, P., Lasdon, L., Engquist, M.: A Reduced gradient algorithm for nonlinear network problems. ACM Trans. Math. Softw. 9, 57\u201370 (1983)","journal-title":"ACM Trans. Math. Softw."},{"key":"366_CR5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BFb0121158","volume":"30","author":"A Bihain","year":"1987","unstructured":"Bihain, A, Nguyen, V H, Strodiot, J. J.: Reduced subgradient algorithm. Math. Program. Study. 30, 127\u2013149 (1987)","journal-title":"Math. Program. Study."},{"key":"366_CR6","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/978-1-4613-0279-7_31","volume":"54","author":"M Bouhadi","year":"2001","unstructured":"Bouhadi, M., Ellaia, R., Souza de Cursi, J. E.: Random perturbations of the projected gradient for linearly constrained problems. Advances in convex analysis and global optimization. Honoring the memory of C. Caratheodory (1873\u20131950). Dordrecht, Kluwer Academic Publishers. Nonconvex Optim. Appl. 54, 487\u2013499 (2001)","journal-title":"Nonconvex Optim. Appl."},{"key":"366_CR7","volume-title":"Proceeding of Winter Simulation Conference, USA","author":"Y Carson","year":"1997","unstructured":"Carson, Y., Maria, A.: Simulation optimization: methods and applications Proceeding of Winter Simulation Conference, USA (1997)"},{"key":"366_CR8","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.neucom.2015.04.033","volume":"167","author":"H Che","year":"2015","unstructured":"Che, H., Li, C., He, X., Huang, T.: An intelligent method of swarm neural networks for equalities constrained nonconvex optimization. Neurocomputing 167, 569\u2013577 (2015)","journal-title":"Neurocomputing"},{"key":"366_CR9","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/BF02591957","volume":"31","author":"RS Dembo","year":"1985","unstructured":"Dembo, R. S.: Dealing with degeneracy in reduced gradient algorithms. Math. Program. 31, 375\u2013363 (1985)","journal-title":"Math. Program."},{"issue":"4","key":"366_CR10","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1137\/0328048","volume":"28","author":"CCY Dorea","year":"1990","unstructured":"Dorea, C. C. Y.: Stopping rules for a random optimization method. SIAM J. Control Optim. 28(4), 841\u2013850 (1990)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"366_CR11","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s11590-010-0262-2","volume":"6","author":"A El Mouatasim","year":"2012","unstructured":"El Mouatasim, A., Ellaia, R., Al-Hossain, A.: A continuous approach to combinatorial optimization: application to water system pump operations. Optim. Lett. J. 6(1), 177\u2013198 (2012)","journal-title":"Optim. Lett. J."},{"key":"366_CR12","first-page":"198","volume":"226","author":"A El Mouatasim","year":"2014","unstructured":"El Mouatasim, A., Ellaia, R., Souza de Cursi, J. E.: Stochastic perturbation of reduced gradient & GRG methods for nonconvex programming problems. Int. J. Appl. Math. Comput. 226, 198\u2013211 (2014)","journal-title":"Int. J. Appl. Math. Comput."},{"key":"366_CR13","doi-asserted-by":"crossref","unstructured":"Floudas, C. A., Pardalos, P. M.: A collection of test problems for constrained global optimization algorithms. Lecture Notes in Computer Science, vol. 455. Springer-Verlag, Berlin (1990)","DOI":"10.1007\/3-540-53032-0"},{"issue":"4","key":"366_CR14","doi-asserted-by":"crossref","first-page":"10441","DOI":"10.1137\/S1052623495290660","volume":"9","author":"NI Gould","year":"1999","unstructured":"Gould, N. I.: On modified factorization for large-scale linearly constrained optimization. SIAM J. Optim. 9(4), 10441\u20131063 (1999)","journal-title":"SIAM J. Optim."},{"key":"366_CR15","doi-asserted-by":"crossref","unstructured":"Griva, I., Nash, S. G., Sofer, A.: Linear and nonlinear optimization. SIAM ISBN 978-0-898716-61-0 (2009)","DOI":"10.1137\/1.9780898717730"},{"key":"366_CR16","doi-asserted-by":"crossref","unstructured":"Hock, W., Schittkowski, K.: Test examples for nonlinear programming codes, Lecture Notes in Economics and Mathematical Systems, 187, Springer (1981)","DOI":"10.1007\/978-3-642-48320-2"},{"key":"366_CR17","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF02239754","volume":"42","author":"T Horst","year":"1989","unstructured":"Horst, T.: Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems. Computing 42, 271\u2013289 (1989)","journal-title":"Computing"},{"key":"366_CR18","unstructured":"Huard, P.: Un algorithme g\u00e9n\u00e9ral de gradient r\u00e9duit [Ageneral reduced gradient algorithm]. Bulletin de la Direction des Etudes et Recherches, electricit\u00e9 de France, S\u00e9,rie C. 2 91\u2013109 (1982)"},{"issue":"1","key":"366_CR19","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1134\/S1995423910010039","volume":"3","author":"EA Kotel\u2019nikov","year":"2010","unstructured":"Kotel\u2019nikov, E. A.: Applying a reduced gradient in quadratic programming. Numer. Anal. Appl. 3(1), 17\u201324 (2010)","journal-title":"Numer. Anal. Appl."},{"issue":"1","key":"366_CR20","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/B:STCO.0000009417.88960.81","volume":"14","author":"P L\u2019Ecuyer","year":"2003","unstructured":"L\u2019Ecuyer, P., Touzin, R: On the Deng-Lin random number generators and related methods. Stat. Comput. 14(1), 5\u20139 (2003)","journal-title":"Stat. Comput."},{"key":"366_CR21","unstructured":"Lacoste-Julien, S.: Convergence rate of Frank-Wolfe for non-convex objectives. arXiv: 1607.00345v1 (2016)"},{"key":"366_CR22","volume-title":"Proceedings of the Conference on Numerical Analysis, Dundee, Scotland","author":"A Levy","year":"1977","unstructured":"Levy, A., Montalvo, A: The tunneling algorithm for the global minimization of functions Proceedings of the Conference on Numerical Analysis, Dundee, Scotland (1977)"},{"key":"366_CR23","doi-asserted-by":"crossref","first-page":"10909","DOI":"10.1016\/j.amc.2013.04.055","volume":"219","author":"C Li","year":"2013","unstructured":"Li, C., Li, D.: An extension of the Fletcher\u2013Reeves method to linear equality constrained optimization problem. Appl. Math. Comput. 219, 10909\u201310914 (2013)","journal-title":"Appl. Math. Comput."},{"key":"366_CR24","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/BF01588966","volume":"14","author":"K Masden","year":"1978","unstructured":"Masden, K., Schjaer-Jacobsen, H.: Linearly constrained minimax optimization. Math. Program. 14, 208\u2013223 (1978)","journal-title":"Math. Program."},{"key":"366_CR25","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.ins.2014.03.059","volume":"285","author":"R Nanuclef","year":"2014","unstructured":"Nanuclef, R., Frandi, E., Sartori, C., Allende, H.: A novel Frank\u2013Wolfe algorithm. Analysis and applications to large-scale SVM training. Inform. Sci. 285, 66\u201399 (2014)","journal-title":"Inform. Sci."},{"key":"366_CR26","unstructured":"Nikolaou, N.: Fast Optimization of Non-Convex Machine Learning Objectives. Master thesis, University of Edinburgh (2012)"},{"issue":"1","key":"366_CR27","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/TAC.1999.5401147","volume":"44","author":"P Sadegh","year":"1999","unstructured":"Sadegh, P., Spall, J. C.: Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 44(1), 231\u2013232 (1999)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"80","key":"366_CR28","first-page":"3963","volume":"77","author":"P Sumathi","year":"2013","unstructured":"Sumathi, P., Paulraj. S.: Identification of redundant constraints in large scale linear programming problems with minimal computational effort. Appl. Math Sci. 77(80), 3963\u20133974 (2013)","journal-title":"Appl. Math Sci."},{"key":"366_CR29","first-page":"85","volume":"104","author":"F Wang","year":"1999","unstructured":"Wang, F., Su, C., Liu, Y.: Computation of optimal feedforward and feedback control by a modified reduced gradient method. Appl. Math. Comput. 104, 85\u2013100 (1999)","journal-title":"Appl. Math. Comput."},{"key":"366_CR30","unstructured":"Wolfe, P: The reduced gradient method. Rand Document. Santa Monica, CA (1962)"},{"key":"366_CR31","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.cam.2016.12.021","volume":"317","author":"R Ziadi","year":"2017","unstructured":"Ziadi, R., Ellaia, R., Bencherif-Madani, A.: Global optimization through a stochastic perturbation of the Polack-Ribi\u00e8re conjugate gradient method. J. Comput. Appl. Math. 317, 672\u2013684 (2017)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0366-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0366-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0366-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T22:26:08Z","timestamp":1659133568000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0366-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,21]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["366"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0366-1","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2017,6,21]]}}}