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Unformatted text preview: ISE 536–Fall03: Linear Programming and Extensions November 19, 2003 Lecture 21: Interior Point Methods Lecturer: Fernando Ord´ o˜nez 1 Complexity of LP The Klee-Minty example says: To measure the efficiency of an algorithm, we need: • Size of an instance. For example, consider the LP: min c t x s . t . Ax = b x ≥ Size is: • Count number of elementary operations, (use O ( · ) notation to simplify the count.) For example, the number of operations of the simplex method in the Klee-Minty example is: What about the number of operations of the simplex method in the Klee-Minty ex- ample if we start from point (1 ,..., 1)? Two instances of the same size can have different running times! We need: Worst Case running time of algorithm A : The maximum running time of A for instances of a given size. 1 For example: The worst running time over all LPs with n variables, m constraints. Worst-case complexity of the Simplex Method?...
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This note was uploaded on 02/13/2012 for the course ISE 536 taught by Professor Yy during the Spring '05 term at South Carolina.
- Spring '05