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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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- Fall '11
- Optimization, Mathematical optimization, KKT conditions, KKT