Abstract
This chapter is the equivalent for optimization problems of what Chapter 3 is for integration problems. Here we distinguish between two separate uses of computer generated random variables. The first use, as seen in Section 5.2, is to produce stochastic techniques to reach the maximum (or minimum) of a function, devising random explorations techniques on the surface of this function that avoid being trapped in a local maximum (or minimum) but also that are sufficiently attracted by the global maximum (or minimum). The second use, described in Section 5.3, is closer to Chapter 3 in that it approximates the function to be optimized. The most popular algorithm in this perspective is the EM (Expectation-Maximization) algorithm.
“Remember, boy,” Sam Nakai would sometimes tell Chee, “when you’re tired of walking up a long hill you think about how easy it’s going to be walking down.”
—Tony Hillerman, A Thief of Time
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Robert, C.P., Casella, G. (2004). Monte Carlo Optimization. In: Monte Carlo Statistical Methods. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4145-2_5
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