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3.
Y. Wardi 《Journal of Optimization Theory and Applications》1989,61(3):473-485
A stochastic algorithm for finding stationary points of real-valued functions defined on a Euclidean space is analyzed. It is based on the Robbins-Monro stochastic approximation procedure. Gradient evaluations are done by means of Monte Carlo simulations. At each iteratex
i
, one sample point is drawn from an underlying probability space, based on which the gradient is approximated. The descent direction is against the approximation of the gradient, and the stepsize is 1/i. It is shown that, under broad conditions, w.p.1 if the sequence of iteratesx
1,x
2,...generated by the algorithm is bounded, then all of its accumulation points are stationary. 相似文献
4.
José E. Valdés 《Operations Research Letters》2006,34(1):49-52
Components C1 and C2 form a series system. Suppose we can allocate the spare R1 in parallel with C1 and the spare R2 in parallel with C2, or otherwise, allocate R1 with C2 and R2 with C1. In this paper, we compare these two options using hazard rate ordering. 相似文献
5.
Fabio Schoen 《Journal of Global Optimization》1991,1(3):207-228
In this paper stochastic algorithms for global optimization are reviewed. After a brief introduction on random-search techniques, a more detailed analysis is carried out on the application of simulated annealing to continuous global optimization. The aim of such an analysis is mainly that of presenting recent papers on the subject, which have received only scarce attention in the most recent published surveys. Finally a very brief presentation of clustering techniques is given. 相似文献
6.
Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example. 相似文献
7.
Optimization technologies and environmental applications 总被引:1,自引:0,他引:1
8.
A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections
of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce
computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with
the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to
a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results. 相似文献
9.
A new stochastic method of reconstructing porous media 总被引:1,自引:0,他引:1
We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional
micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing
both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected
completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program.
We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability
function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability.
The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice
Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy
and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore
space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than
0.2 to ensure its connectivity and conductivity. 相似文献
10.
A stochastic approximation algorithm for estimating multichannel coefficients is proposed, and the estimate is proved to converge to the true parameters a.s. up-to a constant scaling factor. The estimate is updated after receiving each new observation, so the output data need not be collected in advance. The input signal is allowed to be dependent and the observation is allowed to be corrupted by noise, but no noise statistics are used in the estimation algorithm. 相似文献