Trosset, M.W. and Torczon, V. 1997, "Numerical optimization using computer experiments," Technical Report 97--38, ICASE, NAS, Langley Research Center, Hampton, VA 23681 --2199.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....with dimension precludes truly global methods in more than a few dimensions for most non convex objective functions, regardless of cost. Despite this, it may be possible to design a model management algorithm to be less sensitive to local minimizers. We cite Kelley [41] and Trosset and Torczon [73] as examples. The next chapter addresses the theoretical issues of the definition and convergence analysis of the model management framework. Subsequent chapters deal with the practical issues of algorithm design and software implementation and present numerical results of an example ....

....near a solution to get an accurate answer, the a priori accuracy would have to be high. Inevitably much of the work in building such a model would go to waste because the accuracy ultimately would be needed only in the part of the space containing a solution. This is addressed in more detail in [73]. 2.4.2 Extending the decomposition of the exploratory moves The previous section presented some general ideas about the use of models and model management for exploratory moves algorithms. Section 2.3.2 presented a simple de 42 composition of the exploratory moves algorithm. In this section ....

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Michael W. Trosset and Virginia Torczon. Numerical optimization using computer experiments. Technical Report 97--38, ICASE, NASA Langley Research Center, Hampton, VA 23681--0001, August 1998. Submitted to Technometrics.

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M.W. Trosset and V. Torczon. Numerical optimization using computer experiments. ICASE TR 9738, Institute for Computer Applications in Science and Engineering, NASA Lanley Research Center, Hampton, Virginia.

....point on the boundary of the feasible region, we must ensure that the lattice manifest in Theorem 3.2 actually allows iterates to land on the boundary. This requires additional but straightforward conditions on such quantities as x 0 , #, # 0 , and the pattern matrices P k (see, for instance, [17]) A related but more subtle di#culty is that the relative sizes of the steps in the core pattern and the remaining points in the pattern must obey certain relations in order to ensure that the algorithm does not take a purely interior approach to a point on the boundary. This rules out, for ....

M. W. Trosset and V. Torczon, Numerical optimization using computer experiments, Tech. Rep. TR97-02, Department of Computational and Applied Mathematics, Rice University, March 1997. Submitted to Technometrics.

....computing environment. Pattern search methods also are less likely to be trapped by non global minimizers than are traditional nonlinear optimization algorithms. Furthermore, recent analysis extends their applicability to optimization problems with general nonlinear constraints [9] Our approach [21] synthesizes recent ideas from both the numerical optimization and the computer experiments literature. Given a limited budget of expensive function evaluations that are to be used to solve an engineering optimization problem, we consider how to manage the trade o# between the expense of ....

....new objective values f(x t ) obtained during the course of the optimization in a straightforward fashion, though we will have more to say about potential di#culties. We also can use any of a wide variety of optimization methods to produce a candidate x t . We have used both quasi Newton methods [21] and pattern search methods [3] to find a candidate x t . For simplicity we use the eyeball method for the examples that follow. Again we stress that we insist on a candidate x t that is on the grid to ensure convergence to a stationary point of f . The convergence theory requires strict ....

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M. W. Trosset and V. Torczon, Numerical optimization using computer experiments, Tech. Report 97--38, Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, Virginia 23681--2199, 1997.

....between The Boeing Company, IBM and Rice University that is dedicated to this challenge. A very general model management framework for exploiting surrogate model information for the purpose of optimizing expensive functions has already been proposed by Dennis and Torczon (1996) Recent work by Trosset and Torczon (1997) specializes this framework to models obtained by kriging, the most popular modeling technique in the literature on computer experiments. Acknowledgements The subject of this report was brought to my attention by Indraneel Das and John Dennis. This research was supported in part by AFOSR grant ....

Trosset, M. W. and Torczon, V. (1997). Numerical optimization using computer experiments. Technical Report 97-02, Department of Computational & Applied Mathematics, Rice University, Houston, TX. Submitted for publication.

....Poll is functionally unchanged by the recalibration step that it now includes. 2 The key to a successful implementation of SMF is to define the Search strategy in a way that e#ciently exploits the current approximation s k . One obvious approach is to search for points that minimize s k . In [41], for example, a finite di#erence quasi Newton method was started from the current iterate with s k as the objective function. A more ambitious strategy would be to explore s k globally for multiple prospective basins, e.g. by performing a comprehensive grid search. For the examples in this paper, ....

....points that reside on the mesh M k near the solution(s) thus obtained. A simple implementation of this strategy, in which a finite di#erence quasi Newton method was used to find a local minimizer of the current DACE approximation (see 4) is the model assisted grid search (MAGS) described in [41]. MAGS was intended for situations in which only a relatively small number of function evaluations are permitted. Because it approximates the objective function over the entire feasible region, recalibration of the approximation is made using one new objective value at a time, as these values are ....

Trosset, M. W. and Torczon, V. 1997: Numerical optimization using computer experiments. Technical Report 97--38, ICASE, NASA Langley Research Center, Hampton, Virginia 23681--2199.

....interpolate the observations, and they depend on a set of correlation parameters [20] that we estimated via maximum likelihood estimation (MLE) as in [9] In [13, 9] it is shown that MLE can be thought of as a form of cross validation. This Gaussian process supposition is a convenient fiction ([23]) that provides useful error estimates, termed mean squared errors (mse) derived from the putative underlying Gaussian process. The mse at a point x is the variance of the spatial process at x given the sampled values (observations) Note that the mse approaches 0 as x approaches an observation, ....

Michael W. Trosset and Virginia Torczon. Numerical optimization using computer experiments. Technometrics, 1997. Submitted for publication.

....obtained for free, often accelerating the search by reducing the total number of iterations required. Opportunities for computational parallelism abound and a parallel implementation of a particular class of pattern search methods has been developed [20] In contrast, model assisted grid search [22] exploits methods developed for the design and analysis of computer experiments [15] The idea is to construct approximations to f that can be used to predict a single trial step that is likely to realize simple decrease on the current value of f(x k ) Thus, pattern search methods can also be ....

M. W. Trosset and V. Torczon. Numerical optimization using computer experiments. Technical Report TR97-02, Department of Computational and Applied Mathematics, Rice University, 1997. Submitted for publication.

....Poll is functionally unchanged by the recalibration step that it now includes. 2 The key to a successful implementation of SMF is to define the Search strategy in a way that efficiently exploits the current approximation s k . One obvious approach is to search for points that minimize s k . In [41], for example, a finite difference quasi Newton method was started from the current iterate with s k as the objective function. A more ambitious strategy would be to explore s k globally for multiple prospective basins, e.g. by performing a comprehensive grid search. For the examples in this ....

....points that reside on the mesh M k near the solution(s) thus obtained. A simple implementation of this strategy, in which a finite difference quasi Newton method was used to find a local minimizer of the current DACE approximation (see x4) is the model assisted grid search (MAGS) described in [41]. MAGS was intended for situations in which only a relatively small number of function evaluations are permitted. Because it approximates the objective function over the entire feasible region, recalibration of the approximation is made using one new objective value at a time, as these values are ....

Trosset, M. W. and Torczon, V. 1997: Numerical optimization using computer experiments. Technical Report 97--38, ICASE, NASA Langley Research Center, Hampton, Virginia 23681--2199.

No context found.

Trosset, M.W. and Torczon, V. 1997, "Numerical optimization using computer experiments," Technical Report 97--38, ICASE, NAS, Langley Research Center, Hampton, VA 23681 --2199.

No context found.

Trosset, M. W. and Torczon, V., "Numerical Optimization Using Computer Experiments," Report No. TR97-02, Dept. of Comp. and App. Math., Rice University, Houston, TX, 1997.

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