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61.
We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C
1 transformation. 相似文献
62.
We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series. 相似文献
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The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study 总被引:1,自引:0,他引:1
Bram Verweij Shabbir Ahmed Anton J. Kleywegt George Nemhauser Alexander Shapiro 《Computational Optimization and Applications》2003,24(2-3):289-333
The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time. 相似文献
66.
A.R.ELAMROUSS 《数学学报(英文版)》2005,21(1):129-142
This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations. 相似文献
67.
近年来,决定椭圆型方程系数反问题在地磁、地球物理、冶金和生物等实际问题上有着广泛的应用.本文讨论了二维的决定椭圆型方程系数反问题的数值求解方法.由误差平方和最小原则,这个反问题可化为一个变分问题,并进一步离散化为一个最优化问题,其目标函数依赖于要决定的方程系数.本文着重考察非线性共轭梯度法在此最优化问题数值计算中的表现,并与拟牛顿法作为对比.为了提高算法的效率我们适当选择加快收敛速度的预处理矩阵.同时还考察了线搜索方法的不同对优化算法的影响.数值实验的结果表明,非线性共轭梯度法在这类大规模优化问题中相对于拟牛顿法更有效. 相似文献
68.
A new approach to the robust handling of non‐linear constraints for GAs (genetic algorithms) optimization is proposed. A specific feature of the approach consists of the change in the conventional search strategy by employing search paths which pass through both feasible and infeasible points (contrary to the traditional approach where only feasible points may be included in a path). The method (driven by full Navier–Stokes computations) was applied to the problem of multiobjective optimization of aerodynamic shapes subject to various geometrical and aerodynamic constraints. The results demonstrated that the method retains high robustness of conventional GAs while keeping CFD computational volume to an acceptable level, which allowed the algorithm to be used in a demanding engineering environment. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Grigor'ev S. A. Kalinnikov A. A. Porembskii V. I. Baranov I. E. Borisova E. V. Fateev V. N. 《Russian Journal of Electrochemistry》2004,40(11):1188-1192
A two-dimensional mathematical model for the transport of reactants in a fuel cell with a solid polymer electrolyte is developed. The model is used for analyzing spatial distributions of the concentration of reactants and current density over the cell. The effect of the catalytic-layer activity, reactant speed, bipolar-plate geometry, thickness and porosity of current collector and/or gas-diffusion sublayer, and the reaction mixture composition on the fuel cell efficiency is estimated theoretically and experimentally. 相似文献