An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces

References

• Adelman D., Klabjan D. Computing near optimal policies in generalized joint replenishment. (2005a) . Working paper (draft), University of Chicago, Graduate School of Business, Chicago, ILGoogle Scholar
• Adelman D., Klabjan D. Duality and existence of optimal policies in generalized joint replenishment. Math. Oper. Res. (2005b) 30:28–50Link, Google Scholar
• Bellman R. E., Dreyfus S. E. Functional approximations and dynamic programming. Math. Tables Other Aids to Comput. (1959) 13:247–251Crossref, Google Scholar
• Billingsley P.Convergence of Probability Measures (1968) (John Wiley and Sons, New York) Google Scholar
• Bojanov B., Hakopian H., Sahakian A.Spline Functions and Multivariate Interpolations (1983) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Google Scholar
• Chen V. C., Ruppert D., Shoemaker C. A. Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Oper. Res. (1999) 47:38–53Link, Google Scholar
• Cheney W., Light W.A Course in Approximation Theory (1999) (Brooks/Cole Publishing Company, New York) Google Scholar
• Croxton K., Gendron B., Magnanti T. A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems. Management Sci. (2003) 49:1268–1273Link, Google Scholar
• Davis P.Interpolation and Approximation (1975) (Dover Publications)Google Scholar
• de Farias D. P., Van Roy B. The linear programming approach to approximate dynamic programming. Oper. Res. (2003) 51:850–856Link, Google Scholar
• de Farias D., Van Roy B. On constraint sampling for the linear programming approach to approximate dynamic programming. Math. Oper. Res. (2004) 29:462–478Link, Google Scholar
• D’Epenoux F. Sur un problème de production et de stockage dans l’aléatoire. Revue Francaise Recherche Opérationnelle (1960) 14:3–16Google Scholar
• Ghellinck G. D. Les problèmes de décisions séquentielles. Cahiers Centre d’Etudes Recherche Opérationnelle (1960) 2:161–179Google Scholar
• Glashoff K., Gustafson S.-A.Linear Optimization and Approximation (1983) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Goberna M., López M.Linear Semi-Infinite Optimization (1998) (John Wiley & Sons, New York) Google Scholar
• Hernández-Lerma O., Lasserre J.Discrete-Time Markov Control Processes: Basic Optimality Criteria (1996) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Hernández-Lerma O., Lasserre J. Approximation schemes for infinite linear programs. SIAM J. Optim. (1998a) 8:973–988Crossref, Google Scholar
• Hernández-Lerma O., Lasserre J. Linear programming approximations for Markov control processes in metric spaces. Acta Appl. Math. (1998b) 51:123–139Crossref, Google Scholar
• Hernández-Lerma O., Lasserre J.Further Topics on Discrete-Time Markov Control Processes (1999) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Johnson S. A., Stedinger J. R., Shoemaker C. A., Li Y., Tejada-Guibert J. A. Numerical solution of continuous-state dynamic programs using linear and spline interpolation. Oper. Res. (1993) 41:484–500Link, Google Scholar
• Klabjan D., Adelman D. Existence of optimal policies for semi-Markov decision processes using duality for infinite linear programming. SIAM J. Control Optim. (2006) 44:2104–4122Crossref, Google Scholar
• Langen H.-J. Convergence of dynamic programming models. Math. Oper. Res. (1981) 6:493–512Link, Google Scholar
• Manne A. Linear programming and sequential decisions. Management Sci. (1960) 6:259–267Link, Google Scholar
• Nemhauser G., Wolsey L.Integer and Combinatorial Optimization (1988) (John Wiley & Sons, New York) Crossref, Google Scholar
• Powell W. B., Topaloglu H., Ruszczynski A., Shapiro A. Stochastic programming in transportation and logistics. Handbook in Operations Research and Management Science: Stochastic Programming (2003) (Elsevier, Amsterdam, The Netherlands) Crossref, Google Scholar
• Rudin W.Real and Complex Analysis (1986) (McGraw-Hill, New York) Google Scholar
• Schweitzer P., Seidmann A. Generalized polynomial approximations in Markovian decision processes. J. Math. Anal. Appl. (1985) 110:568–582Crossref, Google Scholar
• Tadic V., Meyn S., Tempo R., Calafiore G., Dabbene F. Randomized algorithms for semi-infinite programming problems. Probabilistic and Randomized Methods for Design Under Uncertainty (2006) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Wang R.-H.Multivariate Spline Functions and Their Applications (1994) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Google Scholar