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

Satoshi Ito | Zendy; SoonYi Wu | Zendy; Ting-Jang Shiu | Zendy; Kok Lay Teo | Zendy

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

Author(s) -

Satoshi Ito,

SoonYi Wu,

Ting-Jang Shiu,

Kok Lay Teo

Publication year - 2009

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2010.6.15

Subject(s) - mathematical optimization , sequence (biology) , linear programming , mathematics , value (mathematics) , dynamic programming , computer science , semi infinite programming , statistics , genetics , biology , geometry , regular polygon

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.

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