{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:13:49Z","timestamp":1762323229429},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,12,3]],"date-time":"2008-12-03T00:00:00Z","timestamp":1228262400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2010,10]]},"DOI":"10.1007\/s10589-008-9221-6","type":"journal-article","created":{"date-parts":[[2008,12,2]],"date-time":"2008-12-02T18:51:02Z","timestamp":1228243862000},"page":"349-376","source":"Crossref","is-referenced-by-count":15,"title":["Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling"],"prefix":"10.1007","volume":"47","author":[{"given":"M.","family":"Baglietto","sequence":"first","affiliation":[]},{"given":"C.","family":"Cervellera","sequence":"additional","affiliation":[]},{"given":"M.","family":"Sanguineti","sequence":"additional","affiliation":[]},{"given":"R.","family":"Zoppoli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,12,3]]},"reference":[{"key":"9221_CR1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF01585511","volume":"7","author":"S.J. Garstka","year":"1974","unstructured":"Garstka, S.J., Wets, R.J.B.: On decision rules in stochastic programming. Math. Program. 7, 117\u2013173 (1974)","journal-title":"Math. Program."},{"key":"9221_CR2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1287\/moor.16.1.119","volume":"16","author":"R.T. Rockafellar","year":"1991","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16, 119\u2013147 (1991)","journal-title":"Math. Oper. Res."},{"key":"9221_CR3","volume-title":"Dynamic Programming","author":"R. Bellman","year":"1957","unstructured":"Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)"},{"key":"9221_CR4","volume-title":"Neuro-Dynamic Programming","author":"D.P. Bertsekas","year":"1996","unstructured":"Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-Dynamic Programming. Athena Scientific, Belmont (1996)"},{"key":"9221_CR5","volume-title":"State Increment Dynamic Programming","author":"R. Larson","year":"1968","unstructured":"Larson, R.: State Increment Dynamic Programming. Elsevier, New York (1968)"},{"key":"9221_CR6","volume-title":"Differential Dynamic Programming","author":"D. Jacobson","year":"1970","unstructured":"Jacobson, D., Mayne, D.: Differential Dynamic Programming. Academic Press, New York (1970)"},{"key":"9221_CR7","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1029\/WR017i006p01565","volume":"17","author":"A. Turgeon","year":"1981","unstructured":"Turgeon, A.: A decomposition method for the long-term scheduling of reservoirs in series. Water Resour. Res. 17, 1565\u20131570 (1981)","journal-title":"Water Resour. Res."},{"key":"9221_CR8","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1029\/96WR02859","volume":"33","author":"T.W. Archibald","year":"1997","unstructured":"Archibald, T.W., McKinnon, K.I.M., Thomas, L.C.: An aggregate stochastic dynamic programming model of multireservoir systems. Water Resour. Res. 33, 333\u2013340 (1997)","journal-title":"Water Resour. Res."},{"key":"9221_CR9","first-page":"155","volume":"17","author":"R. Bellman","year":"1963","unstructured":"Bellman, R., Kalaba, R., Kotkin, B.: Polynomial approximation\u2014A new computational technique in dynamic programming. Math. Comput. 17, 155\u2013161 (1963)","journal-title":"Math. Comput."},{"key":"9221_CR10","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1029\/WR024i008p01345","volume":"24","author":"E. Foufoula-Georgiou","year":"1988","unstructured":"Foufoula-Georgiou, E., Kitanidis, P.K.: Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems. Water Resour. Res. 24, 1345\u20131359 (1988)","journal-title":"Water Resour. Res."},{"key":"9221_CR11","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1287\/opre.41.3.484","volume":"41","author":"S.A. Johnson","year":"1993","unstructured":"Johnson, S.A., Stedinger, J.R., Shoemaker, C., Li, Y., Tejada-Guibert, J.A.: Numerical solution of continuous-state dynamic programs using linear and spline interpolation. Oper. Res. 41, 484\u2013500 (1993)","journal-title":"Oper. Res."},{"key":"9221_CR12","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1287\/opre.49.3.398.11219","volume":"49","author":"C.R. Philbrick Jr.","year":"1999","unstructured":"Philbrick, Jr., C.R., Kitanidis, P.K.: Improved dynamic programming methods for optimal control of lumped-parameter stochastic systems. Oper. Res. 49, 398\u2013412 (1999)","journal-title":"Oper. Res."},{"key":"9221_CR13","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1287\/opre.47.1.38","volume":"47","author":"V.C.P. Chen","year":"1999","unstructured":"Chen, V.C.P., Ruppert, D., Shoemaker, C.A.: Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Oper. Res. 47, 38\u201353 (1999)","journal-title":"Oper. Res."},{"key":"9221_CR14","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1093\/rfs\/14.1.113","volume":"14","author":"F.A. Longstaff","year":"2001","unstructured":"Longstaff, F.A., Schwartz, E.S.: Valuing American options by simulation: A simple least squares approach. Rev. Financ. Stud. 14, 113\u2013147 (2001)","journal-title":"Rev. Financ. Stud."},{"key":"9221_CR15","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0167-6687(96)00004-2","volume":"19","author":"J.F. Carriere","year":"1996","unstructured":"Carriere, J.F.: Valuation of the early-exercise price for derivative securities using simulations and splines. Insur. Math. Econ. 19, 19\u201330 (1996)","journal-title":"Insur. Math. Econ."},{"key":"9221_CR16","doi-asserted-by":"crossref","unstructured":"Brodie, P., Glasserman, M.: A stochastic mesh method for pricing high dimensional American options, J. Comput. Finance 7, 2004","DOI":"10.21314\/JCF.2004.117"},{"key":"9221_CR17","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/978-1-4757-2204-8_15","volume-title":"Systems, Models and Feedback: Theory and Applications","author":"R. Zoppoli","year":"1992","unstructured":"Zoppoli, R., Parisini, T.: Learning techniques and neural networks for the solution of n-stage nonlinear nonquadratic optimal control problems. In: Isidori, A., Tarn, T.J. (eds.) Systems, Models and Feedback: Theory and Applications, pp. 193\u2013210. Birkh\u00e4user, Boston (1992)"},{"key":"9221_CR18","doi-asserted-by":"crossref","unstructured":"Alessandri, A., Parisini, T., Sanguineti, M., Zoppoli, R.: Neural strategies for nonlinear optimal filtering. In: Proc. IEEE Int. Conf. Syst. Eng., Kobe, Japan, 1992, pp. 44\u201349","DOI":"10.1109\/ICSYSE.1992.236946"},{"key":"9221_CR19","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1023\/A:1013662124879","volume":"112","author":"R. Zoppoli","year":"2002","unstructured":"Zoppoli, R., Parisini, T., Sanguineti, M.: Approximating networks and extended Ritz method for the solution of functional optimization problems. J. Optim. Theory Appl. 112, 403\u2013439 (2002)","journal-title":"J. Optim. Theory Appl."},{"key":"9221_CR20","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1109\/18.971754","volume":"48","author":"V. K\u016frkov\u00e1","year":"2002","unstructured":"K\u016frkov\u00e1, V., Sanguineti, M.: Comparison of worst-case errors in linear and neural network approximation. IEEE Trans. Inf. Theory 48, 264\u2013275 (2002)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9221_CR21","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1137\/S1052623403426507","volume":"15","author":"V. K\u016frkov\u00e1","year":"2005","unstructured":"K\u016frkov\u00e1, V., Sanguineti, M.: Error estimates for approximate optimization by the extended Ritz method. SIAM J. Optim. 15, 261\u2013287 (2005)","journal-title":"SIAM J. Optim."},{"key":"9221_CR22","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1109\/TNN.2004.824413","volume":"15","author":"C. Cervellera","year":"2004","unstructured":"Cervellera, C., Muselli, M.: Deterministic design for neural\u2013network learning: An approach based on discrepancy. IEEE Trans. Neural Netw. 15, 533\u2013544 (2004)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR23","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1029\/WR018i004p00673","volume":"18","author":"S. Yakowitz","year":"1982","unstructured":"Yakowitz, S.: Dynamic programming applications in water resources. Water Resour. Res. 18, 673\u2013696 (1982)","journal-title":"Water Resour. Res."},{"issue":"3","key":"9221_CR24","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1016\/j.ejor.2005.01.022","volume":"171","author":"C. Cervellera","year":"2006","unstructured":"Cervellera, C., Chen, V.C., Wen, A.: Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization. Eur. J. Oper. Res. 171(3), 1139\u20131151 (2006)","journal-title":"Eur. J. Oper. Res."},{"key":"9221_CR25","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1029\/WR015i004p00737","volume":"15","author":"S. Gal","year":"1979","unstructured":"Gal, S.: Optimal management of a multireservoir water supply system. Water Resour. Res. 15, 737\u2013749 (1979)","journal-title":"Water Resour. Res."},{"key":"9221_CR26","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1111\/j.1752-1688.1985.tb05383.x","volume":"21","author":"J.D. Salas","year":"1985","unstructured":"Salas, J.D., Tabios III, G.Q., Bartolini, P.: Approaches to multivariate modeling of water resources time series. Water Resour. Bull. 21, 683\u2013708 (1985)","journal-title":"Water Resour. Bull."},{"key":"9221_CR27","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1109\/72.883426","volume":"11","author":"L. Grippo","year":"2000","unstructured":"Grippo, L.: Convergent on-line algorithms for supervised learning in neural networks. IEEE Trans. Neural Netw. 11, 1284\u20131299 (2000)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR28","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1109\/72.991413","volume":"13","author":"A. Alessandri","year":"2002","unstructured":"Alessandri, A., Sanguineti, M.: Optimization-based learning with bounded error for feedforward neural networks. IEEE Trans. Neural Netw. 13, 261\u2013273 (2002)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR29","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10589-007-9047-7","volume":"38","author":"A. Alessandri","year":"2007","unstructured":"Alessandri, A., Cuneo, M., Pagnan, S., Sanguineti, M.: A recursive algorithm for nonlinear least-squares problems. Comput. Optim. Appl. 38, 195\u2013216 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"9221_CR30","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","volume":"39","author":"A.R. Barron","year":"1993","unstructured":"Barron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inf. Theory 39, 930\u2013945 (1993)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9221_CR31","first-page":"115","volume":"14","author":"A.R. Barron","year":"1994","unstructured":"Barron, A.R.: Approximation and estimation bounds for artificial neural networks. Mach. Learn. 14, 115\u2013133 (1994)","journal-title":"Mach. Learn."},{"key":"9221_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2696-8","volume-title":"Stochastic Approximation Algorithms and Applications","author":"H.J. Kushner","year":"1997","unstructured":"Kushner, H.J., Yin, G.G.: Stochastic Approximation Algorithms and Applications. Springer, New York (1997)"},{"key":"9221_CR33","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","volume":"6","author":"M. Leshno","year":"1993","unstructured":"Leshno, M., Ya, V., Pinkus, A., Schocken, S.: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw. 6, 861\u2013867 (1993)","journal-title":"Neural Netw."},{"key":"9221_CR34","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","volume":"3","author":"J. Park","year":"1991","unstructured":"Park, J., Sandberg, I.W.: Universal approximation using radial-basis-function networks. Neural Comput. 3, 246\u2013257 (1991)","journal-title":"Neural Comput."},{"key":"9221_CR35","volume-title":"Principles of Mathematical Analysis","author":"W. Rudin","year":"1976","unstructured":"Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)","edition":"3"},{"key":"9221_CR36","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1016\/j.automatica.2008.02.001","volume":"44","author":"J. Thenie","year":"2008","unstructured":"Thenie, J., Vial, J.P.: Step decision rules for multistage stochastic programming: A heuristic approach. Automatica 44, 1569\u20131584 (2008)","journal-title":"Automatica"},{"key":"9221_CR37","volume-title":"Calculus of Variations","author":"I.M. Gelfand","year":"1963","unstructured":"Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice-Hall, Englewood Cliffs (1963)"},{"key":"9221_CR38","doi-asserted-by":"crossref","unstructured":"Giulini, S., Sanguineti, M.: Approximation schemes for functional optimization problems J. Optim. Theory Appl. doi: 10.1007\/s10957-008-9471-6","DOI":"10.1007\/s10957-008-9471-6"},{"key":"9221_CR39","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/72.286914","volume":"5","author":"T. Parisini","year":"1994","unstructured":"Parisini, T., Zoppoli, R.: Neural networks for feedback feedforward nonlinear control systems. IEEE Trans. Neural Netw. 5, 436\u2013449 (1994)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR40","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1109\/9.506245","volume":"41","author":"R. Zoppoli","year":"1996","unstructured":"Zoppoli, R., Parisini, T.: Neural approximations for multistage optimal control of nonlinear stochastic systems. IEEE Trans. Autom. Control 41, 889\u2013895 (1996)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9221_CR41","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1109\/72.925553","volume":"12","author":"M. Baglietto","year":"2001","unstructured":"Baglietto, M., Parisini, T., Zoppoli, R.: Distributed\u2013information neural control: the case of dynamic routing in traffic networks. IEEE Trans. Neural Netw. 12, 485\u2013502 (2001)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR42","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-1-4613-0241-4_2","volume-title":"High Performance Algorithms and Software for Nonlinear Optimization","author":"M. Baglietto","year":"2003","unstructured":"Baglietto, M., Sanguineti, M., Zoppoli, R.: Facing the curse of dimensionality by the extended Ritz method in stochastic functional optimization: dynamic routing in traffic networks. In: Di Pillo, G., Murli, A. (eds.) High Performance Algorithms and Software for Nonlinear Optimization, pp. 23\u201356. Kluwer Academic, Dordrecht (2003)"},{"key":"9221_CR43","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/10556780512331318245","volume":"20","author":"A. Alessandri","year":"2005","unstructured":"Alessandri, A., Sanguineti, M.: Optimization of approximating networks for optimal fault diagnosis. Optim. Methods Softw. 20, 241\u2013266 (2005)","journal-title":"Optim. Methods Softw."},{"key":"9221_CR44","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1109\/9.867017","volume":"45","author":"L.Y. Wang","year":"2000","unstructured":"Wang, L.Y., Yin, G.G.: Persistent identification of systems with unmodeled dynamics and exogenous disturbances. IEEE Trans. Autom. Control 45, 1246\u20131256 (2000)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9221_CR45","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1162\/neco.1996.8.4.819","volume":"8","author":"P. Niyogi","year":"1996","unstructured":"Niyogi, P., Girosi, F.: On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions. Neural Comput. 8, 819\u2013842 (1996)","journal-title":"Neural Comput."},{"key":"9221_CR46","first-page":"118","volume":"31","author":"M. Nussbaum","year":"1986","unstructured":"Nussbaum, M.: On nonparametric estimation of a regression function that is smooth in a domain on\u00a0\u211d k . Theory Probab. Appl. 31, 118\u2013125 (1986)","journal-title":"Theory Probab. Appl."},{"key":"9221_CR47","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1162\/neco.1995.7.2.219","volume":"7","author":"F. Girosi","year":"1995","unstructured":"Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Comput. 7, 219\u2013269 (1995)","journal-title":"Neural Comput."},{"key":"9221_CR48","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2440-0","volume-title":"The Nature of Statistical Learning Theory","author":"V.N. Vapnik","year":"1995","unstructured":"Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)"},{"key":"9221_CR49","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970081","volume-title":"Random Number Generation and Quasi-Monte Carlo Methods","author":"H. Niederreiter","year":"1992","unstructured":"Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)"},{"key":"9221_CR50","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s10589-007-9054-8","volume":"38","author":"C. Cervellera","year":"2007","unstructured":"Cervellera, C., Muselli, M.: Efficient sampling in approximate dynamic programming algorithms. Comput. Optim. Appl. 38, 417\u2013443 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"9221_CR51","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3095-8","volume-title":"Number-Theoretic Methods in Statistics","author":"K.-T. Fang","year":"1994","unstructured":"Fang, K.-T., Wang, Y.: Number-Theoretic Methods in Statistics. Chapman & Hall, London (1994)"},{"key":"9221_CR52","first-page":"784","volume":"7","author":"I.M. Sobol\u2019","year":"1967","unstructured":"Sobol\u2019, I.M.: The distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisl. Mat. Mat. Fiz. 7, 784\u2013802 (1967)","journal-title":"Zh. Vychisl. Mat. Mat. Fiz."},{"key":"9221_CR53","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","volume":"5","author":"M.T. Hagan","year":"1994","unstructured":"Hagan, M.T., Menhaj, M.: Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw. 5, 989\u2013993 (1994)","journal-title":"IEEE Trans. Neural Netw."},{"key":"9221_CR54","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.jco.2004.11.002","volume":"21","author":"V. K\u016frkov\u00e1","year":"2005","unstructured":"K\u016frkov\u00e1, V., Sanguineti, M.: Learning with generalization capability by kernel methods of bounded complexity. J. Complex. 21, 350\u2013367 (2005)","journal-title":"J. Complex."},{"key":"9221_CR55","doi-asserted-by":"crossref","unstructured":"Gnecco, G., Sanguineti, M.: Accuracy of suboptimal solutions to kernel principal component analysis, Comput. Optim. Appl. doi: 10.1007\/s10589-007-9108-y","DOI":"10.1007\/s10589-007-9108-y"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9221-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-008-9221-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9221-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:35Z","timestamp":1559302595000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-008-9221-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,3]]},"references-count":55,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["9221"],"URL":"https:\/\/doi.org\/10.1007\/s10589-008-9221-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,3]]}}}