MaBOS : Nonlinear Programming

Global Optimization

A typical difficulty associated with nonlinear optimization is the problem that due to the presence of nonconvexities in most cases it is difficult to determine the global optimum. Loosely speaking, the global optimum is the best of all possible values while a local optimum is the best in a nearby neighborhood only.

Global optimization problems are seen to be attacked by stochastic and deterministic solution approaches.

In the group of stochastic methods we find

   genetic algorithms
   evolution strategies
   taboo search
   simulated annealing

In the strict sense these methods are not optimization methods at all because they do not guarantee neither optimality nor a certain quality of the solution.

In contrast, deterministic methods are based on progressive and rigorous reduction of the solution space until the global solution has been determined with a pre-given accuracy. Deterministic methods may be classified as:

   primal-dual methods
   convex underestimators and convex relaxations
   interval methods
   Branch&Bound algorithms

Although, at present the application of deterministic global optimization algorithms seems to be limited to smaller size problems, say, less than 2,000 variables, the field is growing, and depending on the problem it might be worthwile to give it a try.

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