Both application- and theory-oriented scientists are familiar with the root-finding problem. The scientific literature is not only rich in original proposals and tutorials, but also in excellent books--Pasupathy and Kim mention some of them. This valuable overview of the stochastic root-finding problem consists of six sections and an electronic appendix (http://portal.acm.org/citation.cfm?doid=1921598.1921603).

After a short introduction (Section 1), Section 2 offers some examples that motivate the request for efficient root-finding procedures in a stochastic framework, including stochastic optimization problem solving.

Section 3 presents notations and terminology. In Section 4, the authors formulate the stochastic root-finding problem. Section 5 describes methods for solving the problem, giving only stochastic approximation and sample-path methods in detail, including basic convergence theorems, results on convergence rates and sample size, algorithms, implementation details, and comments on their performance. The online appendix describes a third type: parametric/semi-parametric methods. Contributions from many researchers, as well as recent developments by Pasupathy, represent the core of this section. Finally, in Section 6, readers will discover some ideas for future research. (The electronic appendix also includes in-depth discussions on research.)

Readers who are unfamiliar with the stochastic root-finding problem should pay attention to some abbreviations (SPSA and SOP) that the paper uses without explanation, an error in relation (7), and the use of the SP abbreviation in two different contexts (in Sections 5.1 and 5.2).

The references are adequate--many of them are on recent developments that can increase the performance of the existing algorithms. Unfortunately, the paper neglects to cite ten references and the introduction does not clearly state the structure of the online appendix.

This paper is a valuable resource for online readers. It will be especially useful to PhD students and various researchers in modeling and computer simulation.