Space-decomposition minimization method for large-scale minimization problems

✍ Scribed by Chin-Sung Liu; Ching-Hung Tseng

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 822 KB
• Volume: 37
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(99)00088-7

✦ Synopsis

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. (~) 1999 Elsevier Science Ltd. All rights reserved.