LEADER 04669nam 2200601Ia 450 001 9910778201803321 005 20230824181742.0 010 $a1-282-28924-1 010 $a9786612289248 010 $a0-08-095527-4 035 $a(CKB)1000000000789985 035 $a(EBL)452978 035 $a(OCoLC)316568668 035 $a(SSID)ssj0000336919 035 $a(PQKBManifestationID)12061766 035 $a(PQKBTitleCode)TC0000336919 035 $a(PQKBWorkID)10301850 035 $a(PQKB)10429428 035 $a(MiAaPQ)EBC452978 035 $a(EXLCZ)991000000000789985 100 $a20090320d1965 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDynamic programming and the calculus of variations /$fStuart E. Dreyfus 210 1$aNew York :$cAcademic Press,$d1965. 215 $a1 online resource (xix, 248 pages) $cillustrations 225 1 $aMathematics in science and engineering ;$v21 311 0 $a0-12-221850-7 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Dynamic Programming and the Calculus of Variations; Copyright Page; Contents; Preface; Chapter I. Discrete Dynamic Programming; 1. Introduction; 2. An Example of a Multistage Decision Process Problem; 3. The Dynamic Programming solution of the Example; 4. The Dynamic Programming Formalism; 5. Two Properties of the Optimal Value Function; 6. An Alternative Method of Solution; 7. Modified Properties of the Optimal Value Function; 8. A Property of Multistage Decision Processes; 9. Further Illustrative Examples; 10. Terminal Control Problems; 11. Example of a Terminal Control Problem 327 $a12. Solution of the Example; 13. Properties of the Solution of a Terminal Control Problem; 14. Summary; Chapter II. The Classical Variational Theory; 1. Introduction; 2. A Problem; 3. Admissible Solutions; 4. Functions; 5. Functionals; 6. Minimization and Maximization; 7. Arc-Length; 8. The Simplest General Problem; 9. The Maximum-Value Functional; 10. The Nature of Necessary Conditions; 11. Example; 12. The Nature of Sufficient Conditions; 13. Necessary and Sufficient Conditions; 14. The Absolute Minimum of a Functional; 15. A Relative Minimum of a Function 327 $a16. A Strong Relative Minimum of a Functional; 17. A Weak Relative Minimum of a Functional; 18. Weak Variations; 19. The First and Second Variations; 20. The Euler-Lagrange Equation; 21. Example; 22. The Legendre Condition; 23. The Second Variation and the Second Derivative; 24. The Jacobi Necessary Condition; 25. Example; 26. Focal Point; 27. Geometric Conjugate Points; 28. The Weierstrass Necessary Condition; 29. Example; 30. Discussion; 31. Transversality Conditions; 32. Corner Conditions; 33. Relative Summary; 34. Sufficient Conditions; 35. Hamilton-Jacobi Theory 327 $a36. Other Problem Formulations; 37. Example of a Terminal Control Problem; 38. Necessary Conditions for the Problem of Mayer; 39. Analysis of the Example Problem; 40. Two-Point Boundary Value Problems; 41. A Well-Posed Problem; 42. Discussion; 43. Computational Solution; 44. Summary; References to Standard Texts; Chapter III. The Simplest Problem; 1. Introduction; 2. Notation; 3. The Fundamental Partial Differential Equation; 4. A Connection with Classical Variations; 5. A Partial Differential Equation of the Classical Type; 6. Two Kinds of Derivatives 327 $a7. Discussion of the Fundamental Partial Differential Equation; 8. Characterization of the Optimal Policy Function; 9. Partial Derivatives along Optimal Curves; 10. Boundary Conditions for the Fundamental Equation: I; 11. Boundary Conditions: II; 12. An Illustrative Example-Variable End Point; 13. A Further Example-Fixed Terminal Point; 14. A Higher-Dimensional Example; 15. A Different Method of Analytic Solution; 16. An Example; 17. From Partial to Ordinary Differential Equations; 18. The Euler-Lagrange Equation; 19. A Second Derivation of the Euler-Lagrange Equation;20. The Legendre Necessary Condition 410 0$aMathematics in science and engineering ;$v21. 606 $aCalculus of variations 606 $aDynamic programming 606 $aProgramming (Mathematics) 615 0$aCalculus of variations. 615 0$aDynamic programming. 615 0$aProgramming (Mathematics) 676 $a519.92 700 $aDreyfus$b Stuart E$0151 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778201803321 996 $aDynamic programming and the calculus of variations$9346432 997 $aUNINA