Convex Relaxations for Global Optimization Under Uncertainty Described by Continuous Random Variables
Convex Relaxations for Global Optimization Under Uncertainty Described by Continuous Random Variables
复制标题
连续随机变量描述的不确定性下全局优化的凸松弛
DOI：
10.1002/aic.16064
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Joseph K. Scott
中科院分区：
文献类型：
--
作者：
Yu;Joseph K. Scott
本文考虑了不连续随机变量所描述的不确定性的非convex全局优化问题。这些问题在化学过程设计，可再生能源系统，随机模型预测控制等中都出现。在这里，我们将注意力限制在预期价值目标和没有追索决策的问题上。原则上，可以使用空间分支和结合（B＆B）在全球解决此类问题。但是，B＆B需要能够在搜索空间的子间隔内绑定最佳客观值的能力，并且现有技术通常不适用，因为预期价值目标通常不能以封闭形式写入。为了解决这个问题，本文提出了一种用于计算凸的新方法和非convex预期值函数的凹入，可用于获得严格的界限，以用于B＆B中。此外，这些放松遵守了二阶方向收敛性，这足以在标准假设下终止B＆B的有限终止。为三个简单示例显示了经验结果。
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control, etc. Here, we restrict our attention to problems with expected-value objectives and no recourse decisions. In principle, such problems can be solved globally using spatial branch-and-bound (B&B). However, B&B requires the ability to bound the optimal objective value on subintervals of the search space, and existing techniques are not generally applicable because expected-value objectives often cannot be written in closed-form. To address this, this article presents a new method for computing convex and concave relaxations of nonconvex expected-value functions, which can be used to obtain rigorous bounds for use in B&B. Furthermore, these relaxations obey a second-order pointwise convergence property, which is sufficient for finite termination of B&B under standard assumptions. Empirical results are shown for three simple examples.
影响因子：
1.8
作者：
A. Tsoukalas;A. Mitsos
通讯作者：
A. Tsoukalas;A. Mitsos