Sample-path optimization in simulation
WSC '94 Proceedings of the 26th conference on Winter simulation
Retrospective approximation algorithms for stochastic root finding
WSC '94 Proceedings of the 26th conference on Winter simulation
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
A simulation-based approach to two-stage stochastic programming with recourse
Mathematical Programming: Series A and B
Retrospective simulation response optimization
WSC '91 Proceedings of the 23rd conference on Winter simulation
A projected stochastic approximation algorithm
WSC '91 Proceedings of the 23rd conference on Winter simulation
Finding Optimal Material Release Times Using Simulation-Based Optimization
Management Science
Stochastic optimization and the simultaneous perturbation method
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Issues on simulation and optimization II: some issues in multivariate stochastic root finding
Proceedings of the 35th conference on Winter simulation: driving innovation
Finite-sample performance guarantees for one-dimensional stochastic root finding
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
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The stochastic root-finding problem (SRFP) is that of solving a system of q equations in q unknowns using only an oracle that provides estimates of the function values. This paper presents a family of algorithms to solve the multidimensional (q ≥ 1) SRFP, generalizing Chen and Schmeiser's one-dimensional retrospective approximation (RA) family of algorithms. The fundamental idea used in the algorithms is to generate and solve, with increasing accuracy, a sequence of approximations to the SRFP. We focus on a specific member of the family, called the Bounding RA algorithm, which finds a sequence of polytopes that progressively decrease in size while approaching the solution. The algorithm converges almost surely and exhibits good practical performance with no user tuning of parameters, but no convergence proofs or numerical results are included here.