Estimation of Derivatives of Nonsmooth Performance Measures in Regenerative Systems
Published Online:1 Nov 2001https://doi.org/10.1287/moor.26.4.741.10010
References
- Applied Probability and Queues (1987) (Wiley, New York) Google Scholar
- A Guide to Simulation (1987) 2nd Edition(Springer-Verlag, New York) Crossref, Google Scholar
- Convex Analysis and Measurable Multifunctions (1977) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Stochastic optimization of regenerative systems using infinitesimal perturbation analysis. IEEE Trans. Automat. Control (1994) 39(7):1400–1410Crossref, Google Scholar
- A Course in Probability Theory (1974) 2nd Edition(Academic Press, San Diego, CA) Google Scholar
- Optimization and Nonsmooth Analysis (1990) . Reprint, SIAM (originally published by Wiley, New York, 1983)Crossref, Google Scholar
- Integration of correspondences. Proc. Fifth Berkeley Sympos. Math. Statist. Probab. (1966) II:351–372Part IGoogle Scholar
- Vector Measures (1977) (American Mathematical Society, Providence, RI) Crossref, Google Scholar
- Gradient Estimation via Perturbation Analysis (1991) (Kluwer, Norwell, MA) Google Scholar
- Regenerative derivatives of regenerative sequences. Adv. Appl. Probab. (1993) 25:116–139Crossref, Google Scholar
- Gradient estimation for regenerative processes. Proc. 1992 Winter Simulation Conf. (1992) (IEEE Press, Piscataway, NJ) 280–288Crossref, Google Scholar
- Optimization of stochastic systems via simulation. Proc. 1989 Winter Simulation Conf. (1989) (IEEE Press, Piscataway, NJ) 90–105Crossref, Google Scholar
- Likelihood ratio gradient estimation for stochastic recursions. Adv. Appl. Probab. (1995) 27:1019–1053Crossref, Google Scholar
- , Dold A., Eckmann B. Strong laws of large numbers for multivalued random variables. Multifunctions and Integrands (1984) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Integrals, conditional expectations and martingales of multivalued functions. J. Multivariate Anal. (1977) 7:149–182Crossref, Google Scholar
- Convex Analysis and Minimization Algorithms I (1993) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Convex Analysis and Minimization Algorithms II (1993a) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Finding optimal material release times using simulation based optimization. Management Sci. (1999) 45:86–102Link, Google Scholar
- Convexity of sample path performance and strong consistency of infinitesimal perturbation analysis. IEEE Trans. Automat. Control (1992) 37(2):258–262Crossref, Google Scholar
- On the minimization of integral functionals. Funct. Anal. Appl. (1969) 3:218–227Crossref, Google Scholar
- Theory of Extremal Problems (1979) (North-Holland, Amsterdam, The Netherlands) Google Scholar
- Measure and Integral (1988) (Springer-Verlag, New York) Crossref, Google Scholar
- A unified view of the IPA, SF and LR gradient estimation techniques. Management Sci. (1990) 36:1364–1383Link, Google Scholar
- Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state. Management Sci. (1994) 40:1562–1578Link, Google Scholar
- Regeneration in tandem queues. Adv. Appl. Probab. (1981) 13:221–230Crossref, Google Scholar
- General Irreducible Markov Chains and Non-negative Operators (1984) (Cambridge University Press, Cambridge, MA) Crossref, Google Scholar
- Optimization of Stochastic Models (1996) (Kluwer, Norwell, MA) Crossref, Google Scholar
- Sample-path optimization of convex stochastic performance functions. Math. Programming Ser. B (1996) 75:137–176Crossref, Google Scholar
- An embedding theorem for spaces of convex sets. Proc. Amer. Math. Soc. (1952) 3:165–169Crossref, Google Scholar
- Markov Chains (1984) (North-Holland, Amsterdam, The Netherlands) Google Scholar
- Convergence of subdifferentials under strong stochastic convexity. Management Sci. (1995) 41:1397–1401Link, Google Scholar
- Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
- , Gossez J. P., Lami Dozo E. J., Mawhin J., Waelbroeck L. Integral functionals, normal integrands and measurable selections. Nonlinear Operators and the Calculus of Variations (1976) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- On the interchange of subdifferentiation and conditional expectation for convex functionals. Stochastics (1982) 7:173–182Crossref, Google Scholar
- Real Analysis (1988) (Macmillan, New York) Google Scholar
- Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (1993) (John Wiley & Sons, New York) Google Scholar
- On concepts of directional differentiability. J. Optim. Theory Appl. (1990) 66(3):477–487Crossref, Google Scholar
- Nondifferentiability of the steady-state function in discrete event dynamical systems. IEEE Trans. Automat. Control (1994) 39(8):1707–1711Crossref, Google Scholar
- Regeneration and Networks of Queues (1987) (Springer-Verlag, New York) Crossref, Google Scholar
- Perturbation analysis: The state of the art and research issues explained via the GI/G/1 queue. Proc. IEEE (1989) 77:114–137Crossref, Google Scholar
- Single run optimization of discrete event simulations—an empirical study using the M/M/1 queue. IIE Trans. (1989) 21:35–49Crossref, Google Scholar
- Coupling, Stationarity and Regeneration (2000) (Springer-Verlag, New York) Crossref, Google Scholar
- Strong consistency of infinitesimal perturbation analysis for tandem queueing networks. J. Discrete Event Dynamic Systems: Theory and Applications (1991) 1:37–59Crossref, Google Scholar
- Stochastic Modeling and the Theory of Queues (1989) (Prentice-Hall, NJ) Google Scholar

