Sequential Exploration of Unknown Multi-dimensional Functions as an Aid to Optimization

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Abstract
The problem of finding a good approximation to the optimum of an unknown function of several variables in a minimum number of function evaluations is approached by exploring sequentially the domain of interest. At each stage an interpolating function derived from a stochastic process model of the objective function is set up, and this is used to determine the location of the next function evaluation. A balance between exploring unknown regions and optimizing the function in known regions is struck by means of a weighting factor, which varies as new data are accumulated.

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