This article contains a survey of some well known facts about the complexity of global optimization, and also describes some results concerning the average-case complexity .
Consider the following optimization problem. Given a class F of objective functions f defined on a compact subset of d-dimensional Euclidean space, the goal is to approximate the global minimum of f based on evaluation of the function at sequentially selected points. The focus will be on the error after n observations
where f n is the smallest of the first n observed function values (other approximations besides f n are often considered).
Complexity of optimization is usually studied in the worst- or average-case setting. In order for a worst-case analysis to be useful the class of objective functions F must be quite restricted. Consider the case where F is a subset of the continuous functions on a compact set. It is convenient to consider the class F = C r([0, 1]d) of real-valued functions on [0, 1]dwith...
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Calvin, J.M. (2001). Adaptive Global Search . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_4
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DOI: https://doi.org/10.1007/0-306-48332-7_4
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