Numerical Optimization Methods

Question

I am curious if any one has comments on "specific characteristics" of a problem that will deem it to be best solved by a specific optimization method such as SimulatedAnnealing, Random Search, or Diferential Evolution, etc.

Edit: I am familiar with the majority of the Mathematica resources which has some useful comments such as:Random search requires that the objective function be locally continuous, DifferentialEvolution is more suitable for discrete optimization problems since it needs a large gene pool, etc. I wanted a discussion expanding that knowledge based on peoples' experience on when they found one method to be more beneficial than other based on the problem characteristics such as size of solution space, non-linearity, processing speed(time), rate of convergence (iterations), etc.

Ps. Thanks for the resources.

Answer 1

Collecting some links to useful resources from the comments:

• The documentation has a section on global optimization which has a short section devoted to each method.

• Presentation about NMinimize available on the Wolfram Library Archive:

  1. Numerical Optimization in Mathematica: An Insider's View of NMinimize

  2. NumericalMath`NMinimize: A New Standard Package for Global Optimization

  3. Numerical Optimization

Answer 2

Mathematica Learning Center has a nice tutorial about Constrained Optimization and Unconstrained Optimization available in ebook format (PDF).

You can find more resources in the learning center if you search for "numerical optimization".