Unformatted text preview: Some important theorems • If ∃ a ±nite optimal solution to the LP then ∃ an optimal BFS to the LP. • x ′ optimal to LP does not necessarily imply x ′ is a BFS. • number of BFS’s ≤ number of BS’s ≤ ( n m ) < ∞ . • Simplex applied to an LP in which all BFS are non degenerate implies BFS are not repeated implies Simplex will terminate in a ±nite number of steps. • Simplex applied to an LP in which some BFS are degenerate may result in a BFS being repeated (cycling)....
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- Fall '08
- Optimization, optimal BFS, Degenerate BFS