Stochastic global optimization as a filtering problem. (arXiv:0912.4072v1 [math.NA])

We present a reformulation of stochastic global optimization as a filtering
problem. The motivation behind this reformulation comes from the fact that for
many optimization problems we cannot evaluate exactly the objective function to
be optimized. Similarly, we may not be able to evaluate exactly the functions
involved in iterative optimization algorithms. For example, we may only have
access to noisy measurements of the functions or statistical estimates provided
through Monte Carlo sampling. This makes iterative optimization algorithms
behave like stochastic maps. Naive global optimization amounts to evolving a
collection of realizations of this stochastic map and picking the realization
with the best properties. This motivates the use of filtering techniques to
allow focusing on realizations that are more promising than others. In
particular, we present a filtering reformulation of global optimization in
terms of a special case of sequential importance sampling methods called
particle filters. The increasing popularity of particle filters is based on the
simplicity of their implementation and their flexibility. For parametric
exponential density estimation problems, we utilize the flexibility of particle
filters to construct a stochastic global optimization algorithm which converges
to the optimal solution appreciably faster than naive global optimization.
Several examples are provided to demonstrate the efficiency of the approach.

Published by

Original source : http://arxiv.org/abs/0912.4072...