Find a local minimum of in with parameter , starting from :

First, load the package:

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 .

First, load the package:

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:

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:

Solve for all initial points:

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.