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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 KleeMinty 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 KleeMinty example is: What about the number of operations of the simplex method in the KleeMinty 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. Worstcase 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.
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