Space-decomposition minimization method for large-scale minimization problems

Abstract

This paper introduces a set of new algorithms, called the Space-Decomposition Minimization (SDM) algorithms, that decomposes the minimization problem into subproblems. If the decomposed-space subproblems are not coupled to each other, they can be solved independently with any convergent algorithm; otherwise, iterative algorithms presented in this paper can be used. Furthermore, if the design space is further decomposed into one-dimensional decomposed spaces, the solution can be found directly using one-dimensional search methods. A hybrid algorithm that yields the benefits of the SDM algorithm and the conjugate gradient method is also given. An example that demonstrates application of SDM algorithm to the learning of a single-layer perceptron neural network is presented, and five large-scale numerical problems are used to test the SDM algorithms. The results obtained are compared with results from the conjugate gradient method.