English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 94487/125002 (76%)
Visitors : 29710290      Online Users : 432
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/79649
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/79649

    Authors: Luh, Hsing
    Chuang, Wen-Hua
    Contributors: 應數系
    Keywords: linear programming, gradient projection method, QR factorization, the simplex method, interior-point algorithms
    Date: 2002
    Issue Date: 2015-12-14 17:33:40 (UTC+8)
    Abstract: By geometric viewpoint in search directions of linear programming problems (LP), there are two major approaches: the simplex method and the interior-point algorithm originated from Karmarkar's approach. Many of their variants developed both in theory and applications are still in progress. Roughly speaking, the main difference among them is that the simplex method is devoted for each the exact optimal solution while Karmarkar-based method is computationally fast in approaching to the neighborhood of the optimal solution, but it becomes slow near the optimal point. By the separating hyperplane theorem, we know that the optimal solution of a linear programming problem would locate at the boundary point. However, Karmarkar's algorithm is claimed as an interior-point approach which takes a solution trajectory path through the interior of the feasible region. On the other hand, these algorithms will coincide the zig-zag situation following the trajectory path before attaining the optimal point meanwhile it cannot achieve the optimal point. Therefore, the purpose of this paper is to study a possible approach by combining the interior point and the simplex method. By means of QR factorization, we give a general analysis on Gradient Projection Method(GPM) in solving linear programming problems. Moreover, we prove that a general assumption-technique constraint matrix A of full rank can be relaxed by using our approach. Finally, we analyze the complexity of this approach to ensure that its upper bound is O(n3).
    Relation: Journal of the Chinese Institute of Industrial Engineers, Volume 19, Issue 4, pages 25-38
    Data Type: article
    DOI 連結: http://dx.doi.org/10.1080/10170660209509210
    DOI: 10.1080/10170660209509210
    Appears in Collections:[應用數學系] 期刊論文

    Files in This Item:

    File Description SizeFormat

    All items in 政大典藏 are protected by copyright, with all rights reserved.

    社群 sharing

    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback