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題 名 | Performance Evaluation of Monomial Versus Newton's Method in the Path-Following Algorithm for Solving Geometric Programming Problems=單項法與牛頓法用於內點法求解幾何規劃問題之效率評估 |
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作 者 | 楊旭豪; | 書刊名 | 管理與系統 |
卷 期 | 4:1 1997.01[民86.01] |
頁 次 | 頁111-124 |
分類號 | 319.9 |
關鍵詞 | 點法; 幾何規劃; 牛頓法; 單項法; Path-following algorithm; Geometric programming; Monomial method; Newton's method; |
語 文 | 英文(English) |
中文摘要 | 幾何規劃是數量最佳化的一種技巧,其問題型態是非線性目標函數與非線性限制 式。內點法則是緣由於 Karmarkar 對線性規劃問題所提出的另一種解法方法。由於在應用 內點法時需要解一組非線性方程組,傳統的牛頓法可能是最被廣泛應用的一種方法。有異於 牛法的另一種方法,單項法,則是把多項的非線性方程式化為單項。本文的貢獻是探討使用 單項法在解每一次運算中的 optimality conditions 的非線性方程組時是否能比牛頓法收 斂更快。根據使用電腦程式測試的結果,牛頓法比單項法好,原因是使用單項法所產生的方 程式的結構有illconditioning的問題,因此效果較差。 |
英文摘要 | Geometric programming (GP)is a class of optimization problems with a nonlinear objective function subject to nonlinear constraints. Path-following algorithm (PFA) is one of the interior point methods whose developments were mainly attributed to Karmarkar. This paper investigates the use of the monomial method against Newton's method for solving the optimality conditions at each interation of the path-following method applied to geometric programming problems. Based on the test results, it is found that Newton's method is superior to the monomial method in this context, apparently due to illconditioning of the system of nonlinear equations representing the optimality conditions. |
本系統中英文摘要資訊取自各篇刊載內容。