homework-10

homework-10 - P by applying the denition. 2. Prove that P...

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MthSc810 – Mathematical Programming Fall 2011, Homework #10. Due Thursday, November 10, 2011, 6PM EDT. From the syllabus: homework will be penalized 50% for each day they are late. After two days, they will not be accepted. No exception. Exercise 1. (Slightly modi±ed from midterm II.) Consider the following poly- hedron, where α 1: P = { x R 2 + : αx 1 - x 2 ≥ - 1 , x 1 - αx 2 1 } . 1. Find the extreme rays of
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Unformatted text preview: P by applying the denition. 2. Prove that P is not contained in its recession cone. Exercise 2. (From midterm II). Verify Farkas Lemma for A = p 1 4 2 3 5 1 P and b = (3 , 4) , by checking that exactly one of the two conditions occurs, but not both. Exercise 3. Solve Problem 4.11 from the textbook....
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