Trust region global strategy on unconstrained optimizaiton problems

• Main Author: 黃正一
• Other Authors: 王有禮
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/78443250362526274844

博士 === 國立臺灣科技大學 === 電子工程系 === 92 === Tensor method has attracted the researches on related problems for its theoretical interest. This dissertation presents trust region global strategy on unconstrained optimization problems. The first part of this dissertation concentrates on a modified double dogleg trust region global strategy for solving unconstrained optimization problems. We use two new directions to construct a double dogleg curve. In order to compare the performance of our algorithm with previous results, which consist of Newton’s double dogleg algorithm proposed by Dennis and Mei and the tensor method proposed by Schnabel and Chow, we use the test functions proposed by Mor´e et al. Mor´e et al. produced 18 test functions for testing the reliability and robustness of an unconstrained optimization software. In our testing, our algorithm performed significantly better than the previous results in most of the test cases. The second part of this dissertation investigates a tensor hookstep trust region global strategy for solving the unconstrained optimization problems. In order to compare the performance of our algorithm with Newton’s hookstep algorithm, we also use the test functions proposed by Mor´e et al. In our testing, our algorithm performed significantly better than the previous results in most of the test cases. The third part of this dissertation proposes the performance of our modified double dogleg algorithm with our tensor hookstep algorithm. We also use the test functions proposed by Mor´e et al. In our testing, our modified double dogleg algorithm performed slightly better than our tensor hookstep algorithm in most of the test cases. However, our tensor hookstep algorithm sometimes is more reliable than our modified double dogleg algorithm.