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Volumn 36, Issue 4, 1998, Pages 1448-1472

Approximation of infinite-dimensional linear programming problems which arise in stochastic control

Author keywords

Discounted criterion; Linear programming; Long term average criterion; Numerical approximation; Stochastic control

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; LINEAR PROGRAMMING; PROBLEM SOLVING;

EID: 0032122808     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996313367     Document Type: Article
Times cited : (18)

References (23)
  • 2
    • 0030366646 scopus 로고    scopus 로고
    • Occupation measures for controlled Markov processes: Characterization and optimality
    • A.G. BHATT AND V.S. BORKAR, Occupation measures for controlled Markov processes: Characterization and optimality, Ann. Probab., 24 (1996), pp. 1531-1562.
    • (1996) Ann. Probab. , vol.24 , pp. 1531-1562
    • Bhatt, A.G.1    Borkar, V.S.2
  • 3
    • 0001554538 scopus 로고
    • On linear programming in a Markov decision problem
    • E.V. DENARDO, On linear programming in a Markov decision problem, Management Sci., 16 (1970), pp. 281-288.
    • (1970) Management Sci. , vol.16 , pp. 281-288
    • Denardo, E.V.1
  • 4
    • 0009244154 scopus 로고
    • On sequential decisions and Markov chains
    • C. DERMAN, On sequential decisions and Markov chains, Management Sci., 9 (1962), pp. 16-24.
    • (1962) Management Sci. , vol.9 , pp. 16-24
    • Derman, C.1
  • 6
    • 0027656154 scopus 로고
    • Optimal control of switching diffusions with application to flexible manufacturing systems
    • M.K. GHOSH, A, ARAPOSTATHIS, AND S.I. MARCUS, Optimal control of switching diffusions with application to flexible manufacturing systems, SIAM J. Control Optim., 31 (1993), pp. 1183-1204.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 1183-1204
    • Ghosh, M.K.1    Arapostathis, A.2    Marcus, S.I.3
  • 8
    • 0343709723 scopus 로고
    • An algorithm to obtain the maximum solution of the HamiltonJacobi equation
    • Optimization Techniques (Proc. 8th IFIP Conf., Wurzburg, 1977), Part I, Springer-Verlag, New York
    • R. GONZÁLEZ AND E. ROFMAN, An algorithm to obtain the maximum solution of the HamiltonJacobi equation, in Optimization Techniques (Proc. 8th IFIP Conf., Wurzburg, 1977), Part I, Lecture Notes in Control and Inform. Sci. 6, Springer-Verlag, New York, 1978, pp. 109-116.
    • (1978) Lecture Notes in Control and Inform. Sci. , vol.6 , pp. 109-116
    • González, R.1    Rofman, E.2
  • 9
    • 0542362424 scopus 로고
    • Optimal control and replacement with statedependent failure rate: An invariant measure approach
    • A.C. HEINRICHER AND R.H. STOCKBRIDGE, Optimal control and replacement with statedependent failure rate: An invariant measure approach, Ann. Appl. Probab., 3 (1993), pp. 380-402.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 380-402
    • Heinricher, A.C.1    Stockbridge, R.H.2
  • 11
    • 0009258232 scopus 로고
    • Average cost Markov decision processes: Optimality conditions
    • O. HERNÁNDEZ-LERMA, J.C. HENNET, AND J.B. LASSERRE, Average cost Markov decision processes: Optimality conditions, J. Math. Anal. Appl., 158 (1991), pp. 396-406.
    • (1991) J. Math. Anal. Appl. , vol.158 , pp. 396-406
    • Hernández-Lerma, O.1    Hennet, J.C.2    Lasserre, J.B.3
  • 13
    • 0032024929 scopus 로고    scopus 로고
    • Existence of Markov controls and characterization of optimal Markov controls
    • T.G. KURTZ AND R.H. STOCKBRIDGE, Existence of Markov controls and characterization of optimal Markov controls, SIAM J. Control Optim., 36 (1998), pp. 609-653.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 609-653
    • Kurtz, T.G.1    Stockbridge, R.H.2
  • 15
    • 0001257766 scopus 로고
    • Linear programming and sequential decisions
    • A.S. MANNE, Linear programming and sequential decisions, Management Sci., 6 (1960), pp. 259-267.
    • (1960) Management Sci. , vol.6 , pp. 259-267
    • Manne, A.S.1
  • 17
    • 0018999760 scopus 로고
    • Solution of nonlinear control problems in Hilbert spaces by means of linear programming techniques
    • J.E. RUBIO, Solution of nonlinear control problems in Hilbert spaces by means of linear programming techniques, J. Optim. Theory Appl., 30 (1980), pp. 643-661.
    • (1980) J. Optim. Theory Appl. , vol.30 , pp. 643-661
    • Rubio, J.E.1
  • 18
    • 0001301560 scopus 로고
    • The global control of nonlinear diffusion equations
    • J.E. RUBIO, The global control of nonlinear diffusion equations, SIAM J. Control Optim., 33 (1995), pp. 308-322.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 308-322
    • Rubio, J.E.1
  • 19
    • 0001287187 scopus 로고
    • Time-average control of martingale problems: A linear programming formulation
    • R.H. STOCKBRIDGE, Time-average control of martingale problems: A linear programming formulation, Ann. Probab., 18 (1990), pp. 206-217.
    • (1990) Ann. Probab. , vol.18 , pp. 206-217
    • Stockbridge, R.H.1
  • 20
    • 0038952812 scopus 로고
    • Some remarks on the infinite-dimensional problems of linear programming
    • A.M. VERSHIK, Some remarks on the infinite-dimensional problems of linear programming, Russian Math. Surveys, 29 (1970), pp. 117-124.
    • (1970) Russian Math. Surveys , vol.29 , pp. 117-124
    • Vershik, A.M.1
  • 21
    • 0542433589 scopus 로고
    • On the optimality of pure strategies
    • H.M. WAGNER, On the optimality of pure strategies, Management Sci., 6 (1960), pp. 268-269.
    • (1960) Management Sci. , vol.6 , pp. 268-269
    • Wagner, H.M.1
  • 22
    • 0009105592 scopus 로고
    • Linear programming in a Markov chain
    • P. WOLFE AND G.B. DANTZIG, Linear programming in a Markov chain, Oper. Res., 10 (1962), pp. 702-710.
    • (1962) Oper. Res. , vol.10 , pp. 702-710
    • Wolfe, P.1    Dantzig, G.B.2
  • 23
    • 0000209312 scopus 로고
    • On approximation by polygons in the calculus of variations
    • L.C. YOUNG, On approximation by polygons in the calculus of variations, Proc. Roy. Soc. London, Ser. A, 141 (1933), pp. 325-341.
    • (1933) Proc. Roy. Soc. London, Ser. A , vol.141 , pp. 325-341
    • Young, L.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.