NMinimize

Or constraints can be specified:

Use NMinimize for linear objectives and constraints:

Integer constraints can be imposed:

This enforces a convergence criteria and :

This enforces a convergence criteria and , which is not achievable with the default machine-precision computation:

Setting a high WorkingPrecision makes the process convergent:

Record all the points evaluated during the solution process of a function with a ring of minima:

Plot all the visited points that are close in objective function value to the final solution:

Specifying a non-default method could give a better solution:

Steps taken by NMinimize in finding the minimum of the classic Rosenbrock function:

With the working precision set to , by default AccuracyGoal and PrecisionGoal are set to :

NMinimize aims to find a global minimum, while FindMinimum attempts to find a local minimum:

Minimize finds a global minimum and can work in infinite precision:

FindFit can use NMinimize to find the global optimal fit. This sets up a model:

Create a function from the model and parameters, and generate sample points:

By default FindFit only finds the local optimal fit:

Using the NMinimize method finds the global optimal fit:

For nonlinear functions, NMinimize may sometimes find only a local minimum:

Specifying a starting interval can help in achieving a better local minimum:

NMinimize finds a local minimum of a two-dimensional function on a disk:

Specifying a starting interval helps in achieving the global minimum:

Solve cannot work with this system of equations because they are highly nonalgebraic:

Use NMinimize with a trivial objective function to find a solution: