\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2010, Volume 6, Issue 1: 15-28. Doi: 10.3934/jimo.2010.6.15
This issue Previous Article Competitive risk management for online Bahncard problem Next Article A recursive topographical differential evolution algorithm for potential energy minimization

A numerical approach to infinite-dimensional linear programming in $L_1$ spaces

  • 1.

    Department of Mathematical Analysis and Statistical Inference, Institute of Statistical Mathematics, Research Organization of Information and Systems, Tokyo 106-8569

  • 2.

    Department of Mathematics, National Cheng Kung University, Tainan

  • 3.

    Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received:  July 31, 2008
Revised:  June 30, 2009
Published:  December 2009
Abstract Related Papers Cited by
    Abstract
  • An infinite-dimensional linear programming formulated on $L_1$ spaces, problem (P), is studied in this paper. A related optimization problem, general capacity problem (GCAP), is also mentioned in this paper. But we find that the optimal solution does not exist in problem (P). Thus, we approach the optimal value for problem (P) via solving the problem (GCAP). A proposed algorithm is shown that we solve a sequence of semi-infinite subproblems to approach the optimal value of problem (P). The error bound for the difference between the optimal value for problem (P) and optimal value for semi-infinite subproblem is also given in this paper. Finally, numerical examples are implemented and compared with discretization method to show our computational efficiency.
    Mathematics Subject Classification: 90C05; 90C34; 90C59; 65K05.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(103) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences