ParametricIPOPTMinimize
ParametricIPOPTMinimize[f,{x1,…},{x1i0,…},{{x1min,x1max},…},{g1,…},{{g1min,g1max},…},pars]
numerically searches for a local minimum of f in x, starting from x=x0, subject to constraints xj min≤xj≤xj max, gi min≤gi≤gi max, with parameters pars.
更多信息和选项
- To use ParametricIPOPTMinimize, you first need to load it using Needs["IPOPTLink`"].
- ParametricIPOPTMinimize gives results in terms of ParametricFunction objects.
- Parameters can be present in any of the arguments of ParametricIPOPTMinimize, including options. »
- ParametricIPOPTMinimize takes the same options and settings as IPOPTMinimize.
范例
打开所有单元关闭所有单元基本范例 (2)
Find a local minimum of 
in 
with parameter 
, starting from 
:
Set up the parametric minimization problem and obtain a ParametricFunction object:
Since this problem has no constraints, the corresponding arguments were be replaced by {}.
Provide parameter values and obtain an instance of IPOPTData expression:
Extract the minimum value and position from the IPOPTData expression:
Minimize 
, subject to 
and 
starting from 
with parameters 
.
Set up the parametric minimization problem and obtain a ParametricFunction object:
Provide parameter values and obtain an instance of IPOPTData expression:
Extract the minimum value and position from the IPOPTData expression:
Generalizations & Extensions (3)
IPOPTOptions (2)
Use IPOPTOptions to set options as described in the IPOPT library documentation http://www.coin-or.org/Ipopt/documentation/node39.html:
Use "tol" to set the relative error tolerance to 10.^-p:
Check that the relative error is below the goal of 10^-4:
Check that the relative error is below the goal of 10^-6:
Use "max_iter" to set the maximum number of iterations to 5:
The message below indicates that 5 iterations were insufficient to reach the default precision goal of 10^-8:
Setting the iteration limit to 10 gives a better result:
Check that the relative error is below the default goal of 10^-8:
Applications (1)
Find a global minimum by solving a problem with different starting points using the initial point as a parameter in ParametricIPOPTMinimize.
Take a function with multiple local minima over a certain region:
Generate the desired amount of starting points:
Plot the function with the initial points:
Load the package and set up the parametric problem:
Extract the minimal values and their positions from all solution objects:
Collect the solutions with the initial points and sort by the minimum value found to get the global minimum value and point:
Group points by the minimum position. A lattice is used to account for small numerical differences:
Show the initial points colored according to the minimum position. The local minima are pointed to by arrows. The global minimum is shown in red.
文本
Wolfram Research (2016)，ParametricIPOPTMinimize，Wolfram 语言函数，https://reference.wolfram.com/language/IPOPTLink/ref/ParametricIPOPTMinimize.html.
CMS
Wolfram 语言. 2016. "ParametricIPOPTMinimize." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/IPOPTLink/ref/ParametricIPOPTMinimize.html.
APA
Wolfram 语言. (2016). ParametricIPOPTMinimize. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/IPOPTLink/ref/ParametricIPOPTMinimize.html 年