## Dynamic ProgrammingAn introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls "a rich lode of applications and research topics." 1957 edition. 37 figures. |

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### Contents

III | 3 |

IV | 4 |

V | 5 |

VI | 7 |

VII | 9 |

VIII | 10 |

X | 11 |

XI | 12 |

CIII | 205 |

CIV | 207 |

CV | 209 |

CVI | 211 |

CVIII | 214 |

CIX | 215 |

CX | 217 |

CXI | 218 |

XII | 16 |

XIV | 19 |

XV | 20 |

XVI | 22 |

XVII | 25 |

XVIII | 26 |

XIX | 28 |

XX | 29 |

XXI | 30 |

XXII | 31 |

XXIII | 33 |

XXIV | 34 |

XXV | 37 |

XXVI | 38 |

XXVII | 39 |

XXVIII | 40 |

XXIX | 61 |

XXX | 62 |

XXXI | 63 |

XXXIII | 64 |

XXXIV | 65 |

XXXV | 66 |

XXXVI | 69 |

XXXVIII | 71 |

XXXIX | 72 |

XL | 74 |

XLI | 76 |

XLII | 77 |

XLIII | 79 |

XLIV | 81 |

XLV | 83 |

XLVII | 85 |

XLVIII | 86 |

XLIX | 87 |

LII | 88 |

LIII | 90 |

LIV | 115 |

LV | 116 |

LVI | 117 |

LVII | 119 |

LVIII | 121 |

LIX | 122 |

LX | 123 |

LXI | 124 |

LXII | 125 |

LXIII | 132 |

LXIV | 151 |

LXV | 152 |

LXVI | 153 |

LXVII | 154 |

LXVIII | 156 |

LXXI | 157 |

LXXIII | 158 |

LXXIV | 159 |

LXXV | 164 |

LXXVI | 166 |

LXXVII | 169 |

LXXIX | 171 |

LXXXI | 172 |

LXXXII | 173 |

LXXXIV | 176 |

LXXXV | 178 |

LXXXVI | 182 |

LXXXVII | 183 |

LXXXVIII | 184 |

LXXXIX | 187 |

XC | 188 |

XCI | 189 |

XCII | 191 |

XCIII | 192 |

XCV | 193 |

XCVII | 194 |

XCVIII | 197 |

XCIX | 200 |

C | 202 |

CI | 203 |

CII | 204 |

CXII | 221 |

CXIII | 222 |

CXIV | 223 |

CXV | 224 |

CXVII | 226 |

CXVIII | 227 |

CXX | 228 |

CXXI | 229 |

CXXII | 230 |

CXXIII | 231 |

CXXIV | 233 |

CXXV | 234 |

CXXVI | 235 |

CXXVII | 236 |

CXXVIII | 241 |

CXXIX | 242 |

CXXX | 244 |

CXXXI | 245 |

CXXXII | 246 |

CXXXIII | 251 |

CXXXV | 252 |

CXXXVI | 253 |

CXXXVII | 254 |

CXXXVIII | 255 |

CXXXIX | 256 |

CXL | 258 |

CXLI | 260 |

CXLII | 263 |

CXLIII | 264 |

CXLIV | 265 |

CXLV | 266 |

CXLVI | 267 |

CXLVII | 268 |

CXLVIII | 269 |

CXLIX | 270 |

CLI | 271 |

CLII | 272 |

CLIII | 273 |

CLV | 274 |

CLVI | 282 |

CLVII | 283 |

CLVIII | 284 |

CLIX | 285 |

CLX | 286 |

CLXI | 287 |

CLXIII | 288 |

CLXIV | 289 |

CLXV | 291 |

CLXVI | 292 |

CLXVII | 294 |

CLXVIII | 295 |

CLXIX | 297 |

CLXX | 299 |

CLXXI | 300 |

CLXXIII | 302 |

CLXXV | 303 |

CLXXVI | 306 |

CLXXVII | 307 |

CLXXVIII | 308 |

CLXXX | 309 |

CLXXXI | 310 |

CLXXXII | 315 |

CLXXXIII | 317 |

CLXXXIV | 319 |

CLXXXV | 320 |

CLXXXVI | 321 |

CLXXXVII | 324 |

CLXXXVIII | 325 |

CXC | 326 |

CXCI | 328 |

CXCII | 330 |

CXCIII | 332 |

CXCV | 334 |

CXCVI | 336 |

CXCVII | 338 |

CXCVIII | 339 |

### Common terms and phrases

allocation analysis analytic approximation in policy assume assumption Bellman calculus of variations Chapter choice computational concave function Consider the problem constraints continuous function convergence convex convex function corresponding cost decision processes defined derive determining the maximum discussion dxjdt Dynamic Programming exer existence and uniqueness expected value finite formulation FULL SCORE functional equation Hence inequality initial interval JV-stage Lemma linear machine mathematical method min-max theorem minimize minimum mixed policy nonlinear obtain optimal policy partial differential equation policy space probability problem of determining problem of maximizing proof quantity RAND Corporation recurrence relation region result satisfies sequence Show solution stage Stieltjes integrals stochastic successive approximations technique theory tion total return uniqueness theorems variables variational problem vector yields