| Summary: | 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.
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