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HW7 - problem Find the dual optimal value and dual optimal...

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ELE 704 Optimization HW7 Due 24 April, 2007 1. Consider the problem minimize x 2 - 5 x + 4 subject to. x 2 - 8 x + 12 0 with x R . (a) Find the feasible set, the optimal value of x and the optimal solution p * of the problem. (b) Plot the objective and constraint functions on the same plot. On this plot show the feasible set, the optimal value and the optimal solution. (c) Plot the Lagrangian L ( x, λ ) for a few values of λ . Verify the lower bound property ( p * inf x L ( x, λ ) for λ 0) . (d) Derive and sketch the Lagrange dual function g ( λ ). (e) State the dual problem, and verify that it is a concave maximization
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Unformatted text preview: problem. Find the dual optimal value and dual optimal solution őĽ * . Find the duality gap. Does strong duality holds? 2. Repeat Q1. for the problem minimize x 2-5 x + 4 subject to. x 2-10 x + 24 ‚ȧ with x ‚ąą R . 3. Find the dual function of the following for x ‚ąą R n minimize q T x subject to Ax ‚Äě b Cx = d Write the dual problem and make the implicit equality constraints explicit. 1...
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