臺灣博碩士論文加值系統

本論文介紹了一種新的全域策略,稱為tensor折線法。這個新的全域策略
可用在解無拘最佳化問題的方法上,特別是tensor法。解無拘最佳化問題
的tensor法最初是由Schanbel和Chow所發展出來的[SIAM J.
Opt.,21(1991) ,pp.293-315],而他們使用尋線法及另外兩種版本的信賴
區域法作為全域策略,不過這兩種信賴區域全域策略的效率並不佳,且太過
於複雜。因此,由 Chow, Eskow,和Schnabel[To appear on ACM
TOMS][SIAM J.Opt.,1993]所發展的無拘最佳化軟體TENMIN只用了尋線法
作為全域策略。在我們的研究中,曾經測試了幾種不同版本的tensor折線
法的演算法,雖然這些演算法的執行效率的差別並不大,但大多比TENMIN
好,最後我們決定了兩種演算法,從測試結果中得知,我們的tensor折線演
算法不只在疊代次數方面,而且在函數求值的次數方面也比傳統的方法好
。

This paper introduced a new global strategy, the tensor dogleg
method, for unconstrained optimization, especially using tensor
methods. Tensor methods for unconstrained optimization were
first introduced by Schnabel and Chow [SIAM J.Opt.,21(1991),
pp.293-315]. They adopted line search method and two version of
trust region methods as global strategies, but these trust
region methods were either inefficient or too complicated.
Therefore, the software package, TENMIN, developed by Chow,
Eskow and Schnabel[To appear on ACM TOMS][SIAM J.Opt.,1993]
employed only the line search method as the global strategy. We
tested several different versions of our tensor dogleg
algorithm. Although the performance of each version of the
algorithm differs slightly, most of them perform better then
TENMIN. We finally introduced two tensor dogleg algorithm and
according the testing data, not only the number of iterations
but also the function evaluation, our algorithms are better
than the conventional method.