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# lect21 - ISE 536Fall03 Linear Programming and Extensions...

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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 0 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

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For example: The worst running time over all LPs with n variables, m constraints. Worst-case complexity of the Simplex Method? Is there and algorithm that is polynomial for LP?
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