Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers

References

• Blum J. R. Approximation methods which converge with probability one. Ann. Math. Statist. (1954) 25:382–386Crossref, Google Scholar
• Chin Daniel C. Comparative study of stochastic algorithms for system optimization based on gradient approximations. IEEE Trans. Systems, Man, Cybernetics, Part B (1997) 27:244–249Crossref, Google Scholar
• Fabian Václav. On asymptotic normality in stochastic approximation. Ann. Math. Statist. (1968) 39(4):1327–1332Crossref, Google Scholar
• Gal S., Rubinstein R. Y., Ziv A. On the optimality and efficiency of common random numbers. Math. Comput. Simulation (1984) 26:502–512Crossref, Google Scholar
• Glasserman Paul, Yao David D. Some guidelines and guarantees for common random numbers. Management Sci. (1992) 38(6):884–908Link, Google Scholar
• Iri Masao, Griewank Andreas, Corliss George F. History of automatic differentiation and rounding error estimation. Automatic Differentiation of Algorithms: Theory, Implementation, Application (1991) (SIAM, Philadelphia, PA) 3–16Google Scholar
• Juedes David W., Griewank Andreas, Corliss George F. A taxonomy of automatic differentiation tools. Automatic Differentiation of Algorithms: Theory, Implementation, Application (1991) (SIAM, Philadelphia, PA) 315–329Google Scholar
• Kiefer J., Wolfowitz J. Stochastic estimation of a regression function. Ann. Math. Statist. (1952) 23:462–466Crossref, Google Scholar
• Kleinman Nathan L., Hill Stacy D., Ilenda Victor A. SPSA/SIMMOD optimization of air traffic delay cost. Proc. Amer. Control Conf. (1997) Albuquerque, New Mexico(June):1121–1125Crossref, Google Scholar
• Kushner Harold J., Clark Dean S.Stochastic Approximation Methods for Constrained and Unconstrained Systems (1978) (Springer-Verlag, New York) Crossref, Google Scholar
• L'Ecuyer Pierre, Perron Gaétan. On the convergence rates of IPA and FDC derivative estimators for finite-horizon stochastic simulations. Oper. Res. (1994) 42(4):643–656Link, Google Scholar
• L'Ecuyer Pierre, Yin George. Budget-dependent convergence rate of stochastic approximation. SIAM J. Optim. (1998) 8(February):217–247Crossref, Google Scholar
• Robbins H., Monro S. A stochastic approximation method. Ann. Math. Statist. (1951) 22:400–407Crossref, Google Scholar
• Sadegh Payman, Spall James C. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automatic Control (1998) 43:1480–1484Correction in 44 231, 1999Crossref, Google Scholar
• Soulié Edgar J., Griewank Andreas, Corliss George F. User's experience with FORTRAN compilers in least squares problems. Automatic Differentiation of Algorithms: Theory, Implementation, and Application (1991) (SIAM, Philadelphia, PA) 297–306Google Scholar
• Spall James C. A stochastic approximation technique for generating maximum likelihood parameter estimates. Proc. Amer. Control Conf. (1987) 1161–1167Google Scholar
• Spall James C. A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting. Proc. IEEE Conf. Decision and Control (1988) 1544–1548Crossref, Google Scholar
• Spall James C. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automatic Control (1992) 37(3):332–341Crossref, Google Scholar