Asymptotic analysis of stochastic programs
Annals of Operations Research
Nelder-Mead simplex modifications for simulation optimization
Management Science
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
A scaled stochastic approximation algorithm
Management Science
WSC '96 Proceedings of the 28th conference on Winter simulation
A review of simulation optimization techniques
Proceedings of the 30th conference on Winter simulation
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
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Simulation Modeling and Analysis
Simulation Modeling and Analysis
On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs
SIAM Journal on Optimization
Global Stochastic Optimization with Low-Dispersion Point Sets
Operations Research
A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization
INFORMS Journal on Computing
Feature Article: Optimization for simulation: Theory vs. Practice
INFORMS Journal on Computing
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Variable-sample methods for stochastic optimization
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Retrospective-approximation algorithms for the multidimensional stochastic root-finding problem
Retrospective-approximation algorithms for the multidimensional stochastic root-finding problem
On choosing parameters in retrospective-approximation algorithms for simulation-optimization
Proceedings of the 38th conference on Winter simulation
A testbed of simulation-optimization problems
Proceedings of the 38th conference on Winter simulation
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An introspective on the retrospective-approximation paradigm
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
Convergence properties of direct search methods for stochastic optimization
Proceedings of the Winter Simulation Conference
Root finding via darts: dynamic adaptive random target shooting
Proceedings of the Winter Simulation Conference
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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The stochastic root-finding problem (SRFP) is that of solving a nonlinear system of equations using only a simulation that provides estimates of the functions at requested points. Equivalently, SRFPs seek locations where an unknown vector function attains a given target using only a simulation capable of providing estimates of the function. SRFPs find application in a wide variety of physical settings. We develop a family of retrospective-approximation (RA) algorithms called Bounding RA that efficiently solves a certain class of multidimensional SRFPs. During each iteration, Bounding RA generates and solves a sample-path problem by identifying a polytope of stipulated diameter, with an image that bounds the given target to within stipulated tolerance. Across iterations, the stipulations become increasingly stringent, resulting in a sequence of shrinking polytopes that approach the correct solution. Efficiency results from: (i) the RA structure, (ii) the idea of using bounding polytopes to exploit problem structure, and (iii) careful step-size and direction choice during algorithm evolution. Bounding RA has good finite-time performance that is robust with respect to the location of the initial solution, and algorithm parameter values. Empirical tests suggest that Bounding RA outperforms Simultaneous Perturbation Stochastic Approximation (SPSA), which is arguably the best-known algorithm for solving SRFPs.