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# hwk3 - Hard copy to be submitted in class on the due date...

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CS 525 - Fall 2011 - Homework 3 * assigned 9/21/11 - due 9/28/11 Hand in an annotated diary file, constructed as outlined in the MATLAB Setup handout and in Homework 1. 1. The norm of a vector z is given by k z k = max 1 i m | z i | . The 1 norm of a vector is given by k z k 1 = m X i =1 | z i | . Reformulate the following optimization problems as linear programs in standard form, that is, all variables are nonnegative variables and all general constraints are constraints. (a) minimize k Ax - b k x is the variable and it is free. A is m × n , b is m × 1, x is n × 1. (b) maximize c 0 x subject to k x k 1 δ Ax = b x is the variable and it is free. A is m × n , b is m × 1, x is n × 1, and δ is a constant.

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Unformatted text preview: * Hard copy to be submitted in class on the due date. No late homework accepted. 2. We would like to construct a quadratic polynomial p ( x ) = a + a 1 x + a 2 x 2 with the properties that p (0) ≤ 1, p (1) ≥ 1, all of the coeﬃcients are between-2 and 2, and p (1 / 2) is as large as possible. Write this problem as a linear program in standard form where the variable is the vector of coeﬃcients ( a ,a 1 ,a 2 ). 3. Do exercise 3-1-2. 4. Do exercise 3-2-1. 5. Do exercise 3-3-2. 6. Do exercise 3-3-7. 2...
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hwk3 - Hard copy to be submitted in class on the due date...

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