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The essence of this article lies in a demonstration of the fact that for some random search methods (r.s.m.) of global optimization, the number of the objective function evaluations required to reach a given accuracy may have very slow (logarithmic) growth to infinity as the accuracy tends to...
The problem of optimal experimental design for response optimization is considered. The optimal point (control)x
* of a response surface is to be determined by estimating the response parametersθ from measurements performed at design pointsx
i,i=1,...,N. Classical sequential approaches for...
The multivariate multiextremal optimization problem is considered. Various statistical procedures based on the use of the asymptotic theory of extreme order statistics are thoroughly described. These procedures are used to infer about the maximal value of a function by its values at random...
We consider multidimensional scaling for embedding dimension two, which allows the detection of structures in dissimilarity data by simply drawing two-dimensional figures. The corresponding objective function, called STRESS, is generally nondifferentiable and has many local minima. In this paper...
This paper is concerned with a continuous time stochastic approximation/optimization problem. The algorithm is given by a pair of differential-integral equations. Our main effort is to derive the asymptotic properties of the algorithm. It is shown that ast → ∞, a suitably normalized sequence of...
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network parameters in a closed form. We give similar...
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