hwk9 - u . 5. Consider the quadratic program minimize x c 1...

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CS 525 - Fall 2011 - Homework 9 For extra credit assigned 11/30/11, due 12/8/11 1. Do Exercise 7-1-3 2. Do Exercise 7-2-2 3. (a) Write down the KKT conditions for the problem minimize x 2 1 + x 2 2 + x 2 3 subject to x 1 + x 2 + x 3 1 x 1 - x 2 - x 3 1 x 1 + x 2 - x 3 1 x 0 (b) Find an optimal primal dual pair which solves the KKT condi- tions. 4. Consider the equality constrained least-squares problem minimize k Ax - b k 2 2 subject to Gx = h where A R m × n with rank( A ) = n and G R p × n with rank( G ) = p . Write down the the KKT conditions, and derive expressions for the optimal primal solution ¯ x and dual solution ¯
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Unformatted text preview: u . 5. Consider the quadratic program minimize x c 1 x 1 + c 2 x 2 + c 3 x 3 subject to x 2 1 + x 2 2 + x 2 3 1 Here x is the variable and c 1 , c 2 , and c 3 are constants. (a) Write down the Lagrangian for this problem. Be careful about the sign of the Lagrange multiplier! (b) By minimizing with respect to x , write down the dual problem. (c) Solve the dual problem. (d) Use the dual optimal solution to solve the original quadratic pro-gram. 2...
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hwk9 - u . 5. Consider the quadratic program minimize x c 1...

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