随机优化方法
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
中文|PDF|2005|317页|ISBN:354022723|10.3 MB实践中出现的优化问题涉及随机参数。为了计算鲁棒最优解，即最优解对随机参数变化不敏感，需要确定性替代问题。基于随机数据的分布，并利用决策理论概念，将随机不确定性下的优化问题转化为确定性替代问题。由于发生概率和预期，必须应用近似求解技术。提供了确定性和随机近似方法及其分析性质：泰勒展开、回归和响应面方法、概率不等式、一阶可靠性方法、凸近似/确定性下降方向/有效点、随机近似方法、概率和均值函数微分。给出了迭代求解过程的收敛结果。本站不对文件进行储存，仅提供文件链接，请自行下载，本站不对文件内容负责，请自行判断文件是否安全，如发现文件有侵权行为，请联系管理员删除。
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