Applied dynamic programming

Applied Dynamic Programming

Volumn , Issue , 2015, Pages 1-363

  Bellman, Richard E ^a   Dreyfus, Stuart E ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; MILITARY OPERATIONS;

CALCULUS OF VARIATIONS; CLASSICAL TECHNIQUES; MATHEMATICAL PROBLEMS; MULTI-STAGE DECISION PROCESS; WORLD WAR II;

DYNAMIC PROGRAMMING;

EID: 84954213764     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (298)

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140. H. Weyl, Symmetry, Princeton University Press, Princeton, New Jersey, 1952.
141. R. S. Ledley and L. B. Lusted, "Reasoning foundation of medical diagnosis," Science, vol. 130, 1959, pp. 9-21.
142. N. Mantel, "Principles of Chemotherapeutic screening," Proc. Fourth Berkeley Symposium, University of California Press, Berkeley, California, to appear, in 1962.
143. B. B. Winter, "Optimal diagnostic procedures," IRE Trans, on Reliability and Quality Control, vol. RQC-9, 1960, pp. 13-19.
144. R. Bellman and B. Gluss, "On various versions of the defective coin problem," Information and Control, vol. 4, 1961, pp. 118-131.
145. R. Courant and D. Hilbert, Methods of Mathematical Physics, Interscience Publishers, Inc., New York, 1958.
146. G. A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
147. R. S. Ingarden, "Composite variational problems," Bull, de l'Académie Polonaise des Sciences, Série des sci. math., astr., et phys., vol. 7, 1959, pp. 687-689.
148. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill Book Co., Inc., New York, 1954.
149. R. Bellman, I. Glicksberg, and O. Gross, "On some variational problems occurring in the theory of dynamic programming," Rend. Girc. Mate. Palermo, serie 2, tomo 3, 1954, pp. 1-35.
150. R. Bellman, I. Glicksberg, and O. Gross, "Some problems in the theory of dynamic programming-a smoothing problem," Soo. Indust. Appl. Math., vol. 2, 1954, pp. 82-89.
151. R. Bellman, I. Glicksberg, and O. Gross, "On the 'bang-bang' control problem," Q. Appl. Math., vol. 14, 1956, pp. 11-18.
152. R. Bellman, I. Glicksberg, and O. Gross, "Some non-classical problems in the calculus of variations," Proc. Amer. Math. Soc., vol. 7, 1956, pp. 87-94.
153. R. Bellman, W. H. Fleming, and D. V. Widder, "Variational problems with constraints," Annali di Mate., vol. 41, 1956, pp. 301-323.
154. R. Bellman, "Dynamic programming and a new formalism in the calculus of variations," Proc. Nat. Acad. Sci. USA, vol. 39, 1953, pp. 1077-1082.
155. R. Bellman, "On the application of dynamic programming to variational problems arising in mathematical economics," Proc. Symposium in Calculus of Variations and Applications, McGraw-Hill Book Co., Inc., New York, 1956, pp. 115-138.
156. H. Osborn, "On the foundations of dynamic programming," J. Math, and Mech., vol. 8, 1959, pp. 867-872.
157. R. Bellman, Dynamic Programming of Continuous Processes, The RAND Corporation, Report R-271, 1954.
158. S. Dreyfus, "Dynamic programming and the calculus of variations," J. Math. Anal, and Appl, vol. 1, 1960, pp. 228-239.
159. J. P. LaSalle, "On time-optimal control systems," Proc. Nat. Acad. Sci. USA, vol. 45, 1959, pp. 573-577.
160. R. Bellman, I. Glicksberg, and 0. Gross, "On the 'bang-bang' control problem," Q. Appl. Math., vol. 14, 1956, pp. 11-18.
161. R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, Princeton, New Jersey, 1961.
162. J. P. LaSalle and S. Lefschetz, "Recent Soviet contributions to ordinary differential equations and nonlinear mechanics," J. Math. Anal, and Appl., to appear in vol. 2, 1961.
163. C. A. Desoer, "The bang-bang servo problem treated by variational techniques,",Jn/ormaiicm and Control, vol. 2, 1959, pp. 333-348.
164. C. A. Desoer, "Pontrjagin's maximum principle and the principle of optimality," J. Franklin Inst., vol. 271, 1961, pp. 361-368.
165. S. Dreyfus, "Dynamic programming and the calculus of variations," J. Math. Anal, and Appl, vol. 1, 1960, pp. 228-239.
166. E. T. Whittaker, A Treatise in the Analytic Dynamics of Particles and Rigid Bodies, Cambridge University Press, Cambridge, 1944.
167. R. Bellman, "Functional equations in the theory of dynamic programming •-VI: a direct convergence proof," Ann. Math., vol. 65, 1957, pp. 215-223.
168. H. Osborn, "The problem of continuous programs," Pacific J. Math., vol. 6, 1956, pp. 721-731.
169. L. Fox, The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations, Oxford University Press, Oxford, 1957.
170. L. Collatz, Numerische Behandlung von Differentialgleichungen, Berlin-Gottingen-Heidelberg, second edition, 1955.
171. R. Kalaba, "On nonlinear differential equations, the maximum operation, and monotone convergence," J. Math, and Mech., vol. 8, 1959, pp. 519-574.
172. R. Kalaba, "Dynamic Programming, Fermat's Principle and the Eikonal Equation," Jour. OpticalSoc. America, vol. 51, 1961, pp. 1150-1151.
173. T. Hacker, "Stability of partially controlled motions of an aircraft," J. Aerospace Sci., vol. 28, 1961, pp. 15-26.
174. R. Bellman, "Directions of mathematical research in nonlinear circuit theory," IRE Trans, of Professional Group on Circuit Theory, vol. CT-7, 1960, pp. 542-553.
175. J. V. Breakwell, "The optimization of trajectories," J. Soc. Indust. Appl. Math., vol. 7, 1959.
176. H. J. Kelley, "Gradient theory of optimal flight paths," Amer. Rocket Soc. J., vol. 30, 1960.
177. S. Cartaino and S. Dreyfus, "Application of dynamic programming to the airplane minimum time-to-climb problem," Aero. Rev., 1957.
178. D. E. Okhotsimskii and T. M. Eneev, J. British Interplanetary Soc, January-February 1958.
179. R. Bellman and S. Dreyfus, "An application of dynamic programming to the determination of optimal satellite trajectories," J. British Interplanetary Soc, vol. 17, 1959-60, pp. 78-83.
180. F. T. Smith, The Optimization of Multistage Orbit Transfer Processes by Dynamic Programming, The RAND Corporation, Paper P-2177, 1961.
181. P. I. Welding and J. Stringer, "A problem in vehicle fuel consumption," Oper. Res. Q., vol. 11, 1960, pp. 197-204.
182. R. Bellman, S. Dreyfus, and R. Kalaba, Applications of Dynamic Programming to Space Guidance, Satellites and Trajectories, The RAND Corporation, Paper P-1923, 1960.
183. J. N. Franklin, "The range of a fleet of aircraft," J. Soc. Indust. Appl. Math., vol. 8, 1960, pp. 541-548.
184. S. E. Dreyfus, "The analysis and solution of optimum trajectory problems," Symposium on Mathematical Optimization Techniques, Santa Monica, California, 1960.
185. R. Bellman, I. Glicksberg, and O. Gross, Some Aspects of the Mathematical Theory of Control Processes, The RAND Corporation, Report R-313, 1958.
186. G. Goertzel, "Minimum critical mass and flat flux," J. Nuclear Energy, vol. 2, 1956, pp. 193-201.
187. R. P. Ten-Dyke, "Computation of rocket step weights to minimize initial gross weights," Jet Propulsion, vol. 28, 1958, pp. 338-340.
188. R. Bellman, "A routing problem," Q. Appl. Math., vol. 16, 1958, pp. 87-90.
189. R. E. Greenwood, "Linear graphs and matrices," Texas J. Science, vol. 12, 1960, pp. 105-108.
190. R. Kalaba, "On some communication network problems, combinatorial analysis," Proc. Symposium in Applied Mathematics, vol. 10, 1960, American Math. Soc.
191. M. Pollack, "The maximum capacity route through a network," Operations Research, vol. 8, 1960, pp. 733-736.
192. M. Pollack and N. Wiebenson, "Solutions of the shortest-route problems- a review," Operations Research, vol. 8, 1960, pp. 224-230.
193. L. R. Ford, Jr. and D. R. Fulkerson, "Maximal flow through a network," Canadian J. Math., vol. 8, 1956, pp. 399-404.
194. R. Bellman and R. Kalaba, "On k-th best policies," J. Soc. Indust. Appl. Math., vol. 8, 1960, pp. 582-588.
195. J. Beardwood, J. H. Halton and J. M. Hammersley, "The shortest path through many points," Proc. Cambridge Phil. Soc., vol. 55, 1959, pp. 299-327.
196. T. Arimizu, "Working group matrix in'dynamic model of forest management," J. Japanese Forestry Soc., vol. 40, 1958, pp. 185-190.
197. S. M. Roberts, Dynamic Programming Formulation of the Catalyst Replacement Problem, (to appear).
198. R. Aris, R. Bellman, and R. Kalaba, "Some optimization problems in chemical engineering," Chem. Engr. Progress Symp. Series, vol. 56, 1960, pp. 95-102.
199. R. Aris, The Optimal Design of Chemical Reactors, Academic Press, Inc., New York, 1961.
200. S. Lehman, On the Continuous Simplex Technique, The RAND Corporation, Research Memorandum RM-1386, 1954.
201. R. Bellman, "On bottleneck problems and dynamic programming," Proc. Nat. Acad. Sci. USA, vol. 39, 1953, pp. 947-951.
202. R. Bellman, "Bottleneck problems, functional equations, and dynamic programming," Econometrica, vol. 22, no. 4, 1954.
203. J. von Neumann, "A model of general economic equilibrium," Review of Economic Studies, vol. 13, 1945-46, pp. 1-9.
204. M. Morishima, "Economic expansion and the interest rate in generalized von Neumann models," Econometrica, vol. 28, 1960, pp. 3.52-363.
205. J. G. Kemeny, O. Morgenstern, and G. L. Thompson, "A generalization of the von Neumann model of an expanding economy," Econometrica, vol. 24, 1956, pp. 115-135.
206. K. Marx, Capital, C. Kerr and Co., Chicago, Illinois, 1933, vol. II, Chapters 20 and 21.
207. R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, Princeton, New Jersey, 1961.
208. H. Bateman, "On the control of an elastic fluid," Bull. Amer. Math. Soc, vol. 51, 1945, pp. 601-646.
209. R. Bellman and J. M. Danskin, A Survey of the Mathematical Theory of Time Lag, Retarded Control and Hereditary Processes, The RAND Corporation, Report R-256, 1954
210. R. Bellman and K. L. Cooke, Differential-difference Equations, Academic Press, Inc., New York, 1962.
211. R. Bellman, I. Glicksberg, and O. Gross, "On the 'bang-bang' control problem," Q. Appl. Math., vol. 14, 1956, pp. 11-18.
212. J. P. LaSalle, "On time-optimal control systems," Proc. Nat. Acad. Sci' USA, vol. 45, 1959, pp. 573-577
213. M. Ash, R. Bellman, and R. Kalaba, "On control of reactor shutdown involving minimal xenon poisoning," Nuclear Sci. and Engr., vol. 6, 1959, pp. 152-156.
214. R. Bellman, "Notes on control processes-on the minimum of maximum deviation," Q. Appl. Math., vol. 14, 1957, pp. 419-423.
215. R. Bellman, "Functional equations and maximum range," Q. Appl. Math., vol. 17, 1959, pp. 316-318.
216. R. Bellman, "Some new techniques in the dynamic programming solution of variational problems," Q. Appl. Math., vol. 16, 1958, pp. 295-305.
217. R. Bellman and R. Kalaba, "Reduction of dimensionality, dynamic programming, and control processes," J. Basic Engr., March 1961, pp. 82-84.
218. C. W. Merriam III, "An optimization theory for feedback control system design," Information and Control, vol. 8, 1960, pp. 32-59.
219. A. T. Fuller, "Optimization of non-linear control systems with transient inputs," J. Electronics and Control, vol. 7, 1960, pp. 465-479.
220. E. L. Peterson, Recent Soviet Progress in Adaptive and Optimum Control, Technical Military Planning Operation, SP-121, Santa Barbara, California, 1961.
221. M. Aoki, "On optimal and sub-optimal policies in the choice of control forces for final-value systems," 1960 IRE National Convention Record, part 4, pp. 15-21.
222. R. Pallu de la Barrier, Controle des Systemes Dynamique, Faculte des Science, University of Caen, 1961.
223. M. Aoki, Dynamic Programming and Conditional Response Extrapolation, Second Joint Automatic Control Conference, University of Colorado, 1961.
224. J. Chanugam and G. E. P. Box, Automatic Optimization of Continuous Processes, Department of Math., Princeton University Technical Report No. 38, 1960.
225. L. D. Berkovitz, A Variational Approach to Differential Games, The RAND Corporation, Paper P-2205, 1961.
226. C. M. Kashmar, E. L. Peterson, F. X. Remond, A General Approach to the Numerical Solution of Multi-dimensional Nonlinear Boundary-valued Problems, General Electric Co., Santa Barbara, California, 1960.
227. R. E. Kalaba, Computational Considerations for some Deterministic and Adaptive Control Processes, The RAND Corporaton, Paper P-2210, 1961.
228. R. Beckwith, Analytic and Computational Aspects of Dynamic Programming Processes of High Dimension, Ph.D. Thesis, Purdue University, 1959.
229. R. Bellman, "A mathematical formulation of variational processes of adaptive type," Fourth Berkeley Symposium on Mathematical Statistics and Probability, to appear.
230. R. Bellman and R. Kalaba, "A mathematical theory of adaptive control processes," Proc. Nat. Acad. Sci. USA, vol. 45, 1959, pp. 1288-1290.
231. R. Bellman and R. Kalaba, "On adaptive control processes," IRE National Convention Record, part 4, 1959, pp. 3-11.
232. R. Bellman and R. Kalaba, "Dynamic programming and adaptive control processes: mathematical foundations," IRE Trans, on Automatic Control, vol. AC-5, 1960, pp. 5-10.
233. R. Bellman and R. Kalaba, "On communication processes involving learning and random duration," IRE National Convention Record, part 4, 1958, pp. 16-20.
234. H. W. Grinnell, On the Optimum Utilization of Correlated Data by Decision Schemes in Information Channels, General Electric Company, RM-60-TM-65, Santa Barbara, California, 1960.
235. R. Aris, The Optimal Design of Chemical Reactors, Academic Press Inc., New York, 1961.
236. R. Aris, The Optimum Conditions for a Single Reaction, Department of Chem. Engr., Univ. of Minnesota, Minneapolis, Minn., unpublished.
237. R. Aris, D. F. Rudd, and N. R. Amundson, "On optimum cross-current extraction," Chem. Engr. Science, vol. 12, 1960, p. 88.
238. G. C. Brown and others, Unit Operations, John Wiley and Sons, Inc., New York, 1955.
239. J. S. Dranoff, L. C. Mitten, W. F. Stevens, L. A. Wanninger, Jr., Application of Dynamic Programming to Countercurrent Flow Processes, Technological Inst., Northwestern University, 1960.
240. S. Dreyfus, "Computational aspects of dynamic programming," Operations Research, vol. 5, 1957, pp. 409-415.
241. J. Happel, Chemical Process Economics, John Wiley and Sons, Inc., New York, 1958.
242. J. J. Hur, Chemical Process Economics in Practice, Reinhold, New York, 1956.
243. R. C. Johnson, W. E. Ball, et al., "Mathematics, computers, operations research, and statistics," Indust. and Engr. Chem., vol. 52, 1960, pp. 359-367.
244. R. C. Johnson, S. M. Roberts, and C. A. Pfretzschner, Optimization and its Importance to Chemical Engineering, AIChE Ann. Meeting, San Francisco, California, December 7-9, 1959.
245. M. S. Peters, Plant Design and Economics for Chemical Engineers, McGraw-Hill Book Co., Inc., New York, 1958.
246. S. M. Roberts, Stochastic Models for the Dynamic Programming Formulation of the Catalyst Replacement Problem, Optimization Techniques in Chem. Engr. Symp., New York University, May 18, 1960.
247. H. E. Schwayer, Process Engineering Economics, McGraw-Hill Book Co., Inc., New York, 1955.
248. R. E. Treybal, Mass Transfer Operations, McGraw-Hill Book Co., Inc., New York, 1955.
249. L. A. Wanninger, The Application of Dynamic Programming to a Distillation Column, M. S. Thesis, Northwestern University, August, 1960.
250. W. F. Gruter and B. H. Messikomer, Systematische Ausbeuteberechnung fur isotherme Reaktoren im Falle zusammengestetzer Reaktionen, CIBA, Basel, Switzerland, 1960.
251. W. F. Gruter and B. H. Messikomer, "Optimalgesteze in der chemischen Reaktionstechnik," Helvetica Chimica Acta, vol. 44, pp. 285-298.
252. W. F. Gruter and B. H. Messikomer, "Dynamische Programmierung in derchemischen Technik, die Optimierung chemischer Reaktionsaubeuten," Helvetica Chimica Acta, vol. 43, pp. 2182-2186.
253. W. F. Gruter and B. H. Messikomer, "Optimalgesetze in der chemischen Reaktortechnik," Chimica, vol. 14, 1960, pp. 263-264.
254. S. M. Roberts and J. D. Mahoney, Dynamic Programming Control of a Batch Reaction, 1961.
255. S. M. Roberts, Dynamic Programming Formulation of the Catalyst Replacement Problem, 1961.
256. A. Nomoto, Dynamic Programming Approach to Brachistochronic Program of Batch Process, Case Institute of Technology, 1959.
257. A. Nomoto, Automatization of Dynamic Testing, Case Institute of Technology, 1959.
258. D. S. Adorno, The Asymptotic Theory of Control Systems-Stochastic and Deterministic Processes, Jet Propulsion Lab., Technical Release 34-73, June 30, 1960.
259. M. Freimer, A Dynamic Programming Approach to Adaptive Control Processes, Lincoln Laboratory, No. 54-2, 1959.
260. M. Freimer, Topics in Dynamic Programming-//: Truncated Policies, Lincoln Laboratory, No. 54G-0020, 1960.
261. L. E. Dubins and L. J. Savage, How to Gamble if You Must (to appear).
262. P. Armer, Attitudes Towards Intelligent Machines, The RAND Corporation, Paper P-2114, 1960.
263. R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Book Co., Inc., New York, 1960, Chapter 9
264. R. Bellman, "On the computational solution of liner programming problems involving almost block diagonal matrices," Management Science, vol. 3, 1957, pp. 403-406.
265. R. Bellman and R. Kalaba, "Reduction of dimensionality, dynamic programming and control processes," J. Basic. Engr., vol. 83, 1961, pp. 82-84.
266. N. Levinson, Appendix to N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series, Technology Press and John Wiley and Sons, New York, 1949.
267. R. Bellman, Dynamic Programming and Mean Square Deviation, The RAND Corporation, Paper P-1147, September 13, 1957.
268. R. Bellman, Dynamic Programming and Linear Prediction Theory, The RAND Corporation, Paper P-2308, May 16, 1961.
269. R. E. Kalman, New Methods and Results in Liner Prediction and Filtering Theory, RIAS, Technical Report 61-1, 1960.
270. W. Feller, An Introduction to Probability Theory and its Applications, John Wiley and Sons, New York, 1957.
271. J. G. Kemeny and J. L. Snell, Finite Markov Chains, D. Van Nostrand Co., Princeton, 1960.
272. R. Bellman, Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957, Chapter XI
273. R. Bellman, "A Markovian decision process," J. Math, and Mech., vol. 6, 1957, pp. 679-684.
274. R. A. Howard, Dynamic Programming and Markov Processes, Technology Press and John Wiley and Sons, New York, 1960.
275. S. Dreyfus, "A note on an industrial replacement process," Operational Research Q., vol. 8, 1957, pp. 190-193.
276. P. Rosentiehl and A. Ghouila-Houri, Les choix économiques, décisions séquentielle et simulation, Dunod, Paris, 1960.
277. R. Bellman, F. Ricciardi, D. Malcolm, C. Clark, and C. Craft, On Top-Management Simulation, American Management Assoc., New York, 1957.
278. F. D. Epenoux, "Sur un problème de production et de stockage dans l'aléatoire," Revue Française Recherche Opérationnelle, no. 14, 1960, pp. 3-16.
279. R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, Princeton, New Jersey, 1961
280. R. S. Ledley and L. B. Lusted, "Reasoning foundations of medical diagnosis," Science, vol. 130, 1959, pp. 9-21.
281. B. B. Winter, "Optimal diagnostic procedures," IRE Trans, on Reliability and Quality Control, vol. RQC-9, 1960, pp. 13-19.
282. J. E. Overall and C. M. Williams, "Models for medical diagnosis," Behavioral Science, vol. 6, 1961, pp. 134-141.
283. D. Blackwell, "On the functional equation of dynamic programming," J. Math. Analysis and Appi., vol. 2, 1961.
284. H. Raiffa and R. Schlaifer, Applied Statistical Decision Theory, Harvard Business School, 1961.
285. J. L. Fisher, "A class of stochastic investment problems," Operations Research, vol. 9, 1961, pp. 53-65.
286. R. Bellman and S. Dreyfus, "Functional approximation and dynamic programming," Math. Tables and Other Aids to Computation, vol. 13, 1959, pp. 247-251.
287. C. W. Merriam, III, "An optimization theory for feedback control system design," Information and Control, vol. 3, 1960, pp. 32-59.
288. S. Chandrasekhar, Radiative Transfer, Oxford Univ. Press, 1948.
289. R. Bellman, R. Kalaba, and M. Prestrud, Invariant Imbedding and Radiative Transfer-I: Plane Parallel Slabs of Finite Thickness, The RAND Corporation, to appear.
290. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill Book Co., Inc., New York, 1954.
291. H. W. Kuhn and A. W. Tucker, "Nonlinear programming," Proc. Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1951, pp. 481-492.
292. A. E. Bryson, F. J. Carroll. W. F. Denham, and K. Mikami, "Determination of the lift program that minimizes re-entry heating with acceleration or range constraints using a steepest descent computation procedure," J. Inst. Aerospace Sciences, to be published in 1961.
293. H. J. Kelley, "Gradient theory of optimal flight paths," ARS Journal, vol. 30, no. 10, October 1960.
294. W. Karush, "A queuing model for an inventory problem," Operations Research, vol. 5, 1957, pp. 693-703.
295. W. Karush, A General Algorithm for the Optimal Distribution of Effort, to appear.
296. R. Bellman and W. Karush, "On a new functional transform in analysis: the Maximum Transform," Bull. Amer. Math. Soc, vol. 67, 1961, pp. 501-3.
297. R. Bellman and W. Karush, The Maximum Transform, to appear.
298. R. Bellman, Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.