| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Research Abstract |
The simplex method is one of various approaches to solve a linear program. The simplex method was developed by Dantzig in 1947. It is well known whether there exist pivoting algorithms to solve a linear program in polynomial time. This problem has been considered for years. In this research, we focused on history-based pivoting rules developed by Zadeh to attack the open problem.
(1) Construction of a method to enumerate LP digraphs, which describes a behavior of pivoting algorithms; (2) Analysis of history-based pivoting rules on the LP digraphs; (3) Verification of some conjectures on the number of applying pivoting rules
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