Algorithmic differentiation techniques for global optimization in the COCONUT environment
Algorithmic differentiation techniques for global optimization in the COCONUT environment
复制标题
COCONUT 环境中全局优化的算法微分技术
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. C. Markót
中科院分区：
文献类型：
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作者：
H. Schichl;M. C. Markót
我们描述算法微分，因为它可以用于全局优化算法。我们专注于在COCONUT环境中实现的全局非线性优化的算法微分方法。COCONUT环境将每个可分解优化问题表示为有向无环图（DAG）。在该软件环境中实现的各种推理模块可以用作求解算法的构建块。他们中的许多人使用基于各种形式的算法微分的技术来计算函数或其导数的近似值或包络。COCONUT环境中的算法微分不仅提供点评估，而且还提供高达3阶的导数的范围封装，以及高达2阶的斜率。注意确保正确处理舍入误差。通过将评估例程与约束传播相结合，可以收紧外壳的范围。这种方法的优点和缺陷也概述。
We describe algorithmic differentiation as it can be used in algorithms for global optimization. We focus on the algorithmic differentiation methods implemented in the COCONUT Environment for global nonlinear optimization. The COCONUT Environment represents each factorable optimization problem as a directed acyclic graph (DAG). Various inference modules implemented in this software environment can serve as building blocks for solution algorithms. Many of them use techniques based on various forms of algorithmic differentiation for computing approximations or enclosures of functions or their derivatives. The algorithmic differentiation in the COCONUT Environment not only provides point evaluations but also range enclosures of derivatives up to order 3, as well as slopes up to order 2. Care is taken to ensure that rounding errors are treated correctly. The ranges of the enclosures can be tightened by combining the evaluation routines with constraint propagation. Advantages and pitfalls of this method are also outlined.