Features optimization problems that in practice involve random model parameters
Provides applications from the fields of robust optimal control / design in case of stochastic uncertainty
Includes numerous references to stochastic optimization, stochastic programming and its applications to engineering, operations research and economics

This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems.

Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, and differentiation formulas for probabilities and expectations.

In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.

Content Level » Research

Keywords » calculus - model - optimization problems - regression - response surface methodology - stochastic approximation - stochastic optimization

Related subjects » Computational Intelligence and Complexity - Mathematics - Operations Research & Decision Theory

特点是实践中涉及随机模型参数的优化问题

提供随机不确定性情况下的稳健优化控制/设计领域的应用。

包括大量关于随机优化、随机编程及其在工程、运筹学和经济学中的应用的参考文献。

本书研究了实践中涉及随机模型参数的优化问题。它详细介绍了稳健最优解的计算，即对随机参数变化不敏感的最优解，其中需要有适当的确定性替代问题。基于随机数据的概率分布，并使用决策理论概念，随机不确定性下的优化问题被转换为适当的确定性替代问题。

由于涉及到概率和期望，本书还展示了如何应用近似的解决技术。提供了几种确定性和随机性的近似方法。泰勒扩展方法、回归和响应面方法（RSM）、概率不等式、生存/失败域的多重线性化、离散化方法、凸式近似/确定性下降方向/系数点、随机近似和梯度程序，以及概率和期望的微分公式。

在第三版中，本书进一步发展了随机优化方法。特别是，它现在展示了如何将随机优化方法应用于工程、经济和运筹学中出现的重要具体问题的近似解决。

内容层次 " 研究

关键词 " 微积分-模型-优化问题-回归-响应面方法-随机近似-随机优化

相关学科 " 计算智能与复杂性 - 数学 - 运筹学与决策理论