Global minimum for non linear constrained

Is there any Matlab code for finding global minimum for non linear constrained problems?

[Adam]

If you have the Optimizatoin toolbox, then probably, if not then almost certainly not, other than what you might find on the File Exchange.

Answer 1

[Matt J]

If you have good initial guess of the solution, then you can try fmincon in the Optimization Toolbox. Otherwise, there is the Global Optimization Toolbox, e.g., using the genetic algorithm, ga().

[Walter Roberson]

Note: fmincon is a local optimizer, not a global optimizer. "A good initial guess" would only be sufficient if you happened to start in the right "basin of attraction".

Answer 2

[Reen]

You can give linear and nonlinear constraints to fmincon. You'll need the Optimization toolbox to use the function though. Details about the function can be found here: https://www.mathworks.com/help/optim/ug/fmincon.html. There are a lot of good examples on that page as well.

[Walter Roberson]

Note: fmincon is a local optimizer, not a global optimizer.

Answer 3

[Walter Roberson]

There is no known algorithm to find the global minima of a "black box" non-linear function (that is, one where you effectively cannot examine the algorithm because it is hidden behind a function handle.)

Given any particular minima-finding deterministic algorithm, you could probably construct an example with a global minima it would be unable to find. For example, take the X-Y plane, Z = 0 everywhere exact at some arbitrary infinitesimally small location, Z = -1 : no location you probe would give any information about the minima was, except if you happened to exactly hit the location of the global minima.

The Global Optimization Toolbox provides tools that can be used to try to find minima of surfaces under various assumptions of function behaviour, but they can never promise they have found the global minima.

The tools in the Global Optimization Toolbox include genetic algorithm, pattern search, simulated annealing, along with tools for taking a whole bunch of different starting points for local minimizers.