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Forecast horizon in dynamic family of one-dimensional control problems

Seria
Rozprawy Matematyczne tom/nr w serii: 315 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Sufficient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
3. Definitions and hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4. Properties of arcs and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
5. Dynamic family of optimal controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6. The maximum principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
7. Horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
8. Remarks to horizon theorems. An economic application . . . . . . . . . . . . . . . . . . . . 27
9. Discrete-time linear systems with stochastic parameters. Horizon theorems . . . . . 29
10. Proof of horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
11. Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
  References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 315
Liczba stron
41
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXV
Daty
wydano
1991
otrzymano
1990-05-02
poprawiono
1991-04-09
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland
Bibliografia
  • [1] J. C. Bean and R. L. Smith, Conditions for the existence of planning horizons, Math. Oper. Res. 9 (3) (1984), 391-401.
  • [2] A. Bensoussan, M. Crouhy and J. M. Proth, Mathematical Theory of Production Planning, North-Holland, Amsterdam 1983.
  • [3] C. Bes and J. B. Lasserre, An on-line procedure in discounted infinite horizon stochastic optimal control, J. Optim. Theory Appl. 50 (1) (1986), 61-67.
  • [4] C. Bes and S. P. Sethi, Concepts of forecast and decision horizons: applications to dynamic stochastic optimization problems, Math. Oper. Res. 13 (2) (1967), 295-310.
  • [5] A. Blikle and J. Łoś, Horizon in dynamic programs with continuous time, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 513-519.
  • [6] S. Bylka, Horizon in Optimization Problems on Multigraphs, PWN, Warszawa 1974 (in Polish).
  • [7] S. Bylka, Horizon theorems for the solution of the dynamic lot-size-model, in: New Results in Inventory Research, Chikan (ed.), Akadémiai Kiadó, Budapest 1984, 649-659.
  • [8] S. Bylka and S. P. Sethi, Existence of solution and forecast horizons in dynamic lot-size-model with nondecreasing holding costs, to appear.
  • [9] F. Clark, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York 1983.
  • [10] R. F. Hartl, A forward algorithm for generalized wheat trading model, Z. Oper. Res. 30A (1986), 135-144.
  • [11] R. F. Hartl, A wheat trading model with demand and spoilage, in: Optimal Control Theory and Economic Analysis 3, G. Faichtinger (ed.), North-Holland 1988, 235-244.
  • [12] O. Hernandez-Lerma and J. B. Lasserre, A forecast horizon and a stopping rule for general Markov decision processes, J. Math. Anal. Appl. 132 (1988), 388-400.
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  • [14] W. J. Hopp, J. C. Bean and R. L. Smith, A new optimality criterion for nonhomogeneous Markov decision processes, Oper. Res. 35 (6) (1987), 875-883.
  • [15] J. B. Lasserre and C. Bes, Infinite horizon in nonstationary stochastic optimal control problems. A planning horizon result, IEEE Trans. Automat. Control AC-29 (9) (1984), 836-837.
  • [16] Z. Lieber, An extension to Modigliani and Hohn's planning horizon results, Management Sci. 20 (3) (1973), 319-330.
  • [17] R. A. Lundin and T. E. Morton, Planning horizon for the dynamic lot size model\rm: Zabel vs. protective procedures and computational results, Oper. Res. 23 (4) (1975), 711-734.
  • [18] J. Łoś, Horizon in dynamic programs with discrete time, report No. 4, Inst. Math., Polish Acad. Sci., 1965 (in Polish).
  • [19] J. Łoś, Horizon in dynamic programs, in: Proc. Fifth Berkeley Sympos. on Math. Statistics and Probability, L. M. Le Cam and J. Neyman (eds.), California University Press, 1967, 479-490.
  • [20] J. Łoś, The approximative horizon in von Neumann models of optimal growth, preprint No. 3, Inst. Math., Polish Acad. Sci., 1970.
  • [21] V. F. Magirou, Stockpiling under price uncertainty and storage capacity constraints, European J. Oper. Res. 11 (1982), 233-246.
  • [22] O. L. Mangasarian, Sufficient conditions for the optimal control of nonlinear systems, SIAM J. Control 4 (1966), 139-152.
  • [23] F. Modigliani and F. Hohn, Production planning over time, Econometrica 23 (1955), 46-66.
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  • [26] H. X. Phu, A Solution method for regular optimal control problems with state constraints, J. Optim. Theory Appl. 62 (3) (1989), 487-511.
  • [27] R. Rempała, Horizontal Solution of an Inventory Problem with Stochastic Prices, in: Inventory in Theory and Practice (Budapest 1984), Stud. Prod. Engrg. Econom. 6, Elsevier, Amsterdam 1986, 715-725.
  • [28] R. Rempała, Forecast horizon in nonstationary Markov decision problems, Optimization 20 (6) (1989), 853-857.
  • [29] R. Rempała, Forecast horizon in convex cost inventory model with spoilage, in: Engineering Costs and Production Economics, Elsevier, to appear.
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  • [31] R. Rempała and S. P. Sethi, Existence of decision and forecast horizons for one-dimensional control problems with applications, preprint 437, Inst. Math., Polish Acad. Sci., 1988.
  • [32] J. E. Schochetman and R. L. Smith, Infinite horizon optimization, Math. Oper. Res. 14 (3) (1989), 559-574.
  • [33] S. P. Sethi and S. Bhaskaran, Conditions for the existence of decision horizons for discounted problems in a stochastic environment, Oper. Res. Lett. 4 (2) (1985), 61-64.
  • [34] S. P. Sethi and G. L. Thompson, Optimal Control Theory: Applications to Management Science, Nijhoff, Boston 1981.
  • [35] J. Teng, G. L. Thompson and S. P. Sethi, Strong decision and forecast horizons in a convex production planning problem, Optimal Control Appl. Methods 5 (1984), 319-330.
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  • [37] J. Zabczyk, Lectures in Stochastic Control, Control Theory Center Report No. 125, University of Warwick, 1984.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: Primary 90C39; Secondary 93C75, 90B05, 90B30, 90A16, 90A05.
Identyfikator YADDA
bwmeta1.element.zamlynska-8471af74-6613-4ea2-9e91-e201cfd8e5b8
Identyfikatory
ISBN
83-85116-29-X
ISSN
0012-3862
Kolekcja
DML-PL
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