pyomo 中的概率分布 [英] Probability distributions in pyomo

问题描述

我想在 Pyomo 中解决受约束的 NLP.然而，目标函数包括一个正态分布，其中正态分布的参数包含决策变量，例如像 - (norm.cdf(model.x[0])) 这样的表达式.

I want to solve a constrained NLP in Pyomo. However, the objective function includes a normal distribution where the argument of the normal distribution contains the decision variable, e.g. an expression like - (norm.cdf(model.x[0])).

但我收到此错误:

 Cannot convert object of type 'ndarray' (value = 1) to a numeric value. 

有没有办法在 Pyomo 中处理正态分布?

Is there a way of working with normal distributions in Pyomo?

推荐答案

我已经看到 pyomo 不喜欢某些您可能习惯于在 pyton 或黑盒函数中使用的典型数学(在 pyomo 中优化 Fortran 函数 和 https://groups.google.com/forum/#!topic/pyomo-forum/dK71XrHlBIM).

I have seen that pyomo isn't a fan of some of the typical math you might be used to wanting in pyton or black box functions (Optimizing Fortran function in pyomo and https://groups.google.com/forum/#!topic/pyomo-forum/dK71XrHlBIM).

我认为在这种情况下，您可能需要写出对象中正常 cdf 的近似值(粗略，我知道).我可以建议:

I think in this case you probably will need to write out an approximation of the normal cdf in the object (gross, I know). Might I suggest:

1/(model.x[0]*2.50663)*(1-model.x[0]**-2+3*model.x[0]**-4+15*model.x[0]**-6-105*model.x[0]**-8)

基于这篇文章:https://mathoverflow.net/questions/19404/近似正态分布函数

这是其他选项的很酷的论文:http://www.hrpub.org/download/20140305/MS7-13401470.pdf

Here is a cool paper of other options: http://www.hrpub.org/download/20140305/MS7-13401470.pdf

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