{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:29:09Z","timestamp":1787329749776,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1997,10]]},"abstract":"<jats:p>The dynamic programming (DP) technique rests on a very simple idea, the principle of optimality due to Bellman. This principle is instrumental in solving numerous problems of optimal control. The control law minimizes a cost functional and is determined by using the optimality principle. However, applicability of the optimality principle requires that the cost functional satisfies the property called \"matrix dynamic programming (MDP) property.\" A simple definition of this property will be provided and functionals having it will be considered.<\/jats:p>","DOI":"10.1137\/s0895479895288334","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"818-826","source":"Crossref","is-referenced-by-count":8,"title":["The Matrix Dynamic Programming Property and Its Implications"],"prefix":"10.1137","volume":"18","author":[{"given":"J. P.","family":"Le Cadre","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"O.","family":"Tr\u00e9mois","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"D. P. Bertzekas,\n                      Dynamic Programming, Deterministic and Stochastic Models\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1987."},{"key":"R2","volume-title":"Introduction to stochastic dynamic programming","author":"Ross Sheldon","year":"1983"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2341-0"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/9.14433"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/18.30995"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"J. P. Le Cadre and O. Tr\u00e9mois,\n                      Optimization of the observer motion using dynamic programming\n                      , in Proc. IEEE 1995, Internat. Conf. Acoustics, Speech Signal Proc., Vol. 5, Detroit, MI, 1995, pp. 3567\u20133570.","DOI":"10.1109\/ICASSP.1995.479757"},{"key":"R7","unstructured":"O. 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European Control Conference 93, Grenoble, France, 1993, pp. 1359\u20131364."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939407"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.1985.310617"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1984.1103664"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(85)90194-6"},{"key":"R14","volume-title":"Linear algebra and linear models","author":"Bapat R.","year":"2000"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"R. A. Horn and C. R. Johnson,\n                      Matrix Analysis\n                      , Cambridge University Press, London, 1985.","DOI":"10.1017\/CBO9780511810817"},{"key":"R16","unstructured":"H. Cartan,\n                      Calcul Diff\u00e9rentiel\n                      , Hermann, Paris, 1967."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"M. H. A. Davis and R. B. 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