However we do have matrix upper 26 bounds on the

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Unformatted text preview: of the optimal policy (x-axis), and include the line y = x on the plot. Report the average values of cT xaff (u) and cT x⋆ (u) over your samples. (These are estimates of E cT xaff (u) and E cT x⋆ (u). The first number, by the way, can be found exactly.) 25 4 Duality 4.1 Numerical perturbation analysis example. Consider the quadratic program minimize x2 + 2x2 − x1 x2 − x1 2 1 subject to x1 + 2x2 ≤ u1 x1 − 4x2 ≤ u2 , 5x1 + 76x2 ≤ 1, with variables x1 , x2 , and parameters u1 , u2 . (a) Solve this QP, for parameter values u1 = −2, u2 = −3, to find optimal primal variable values x⋆ and x⋆ , and optimal dual variable values λ⋆ , λ⋆ and λ⋆ . Let p⋆ denote the optimal objective 3 2 1 2 1 value. Verify that the KKT conditions hold for the optimal primal and dual variables you found (within reasonable numerical accuracy). Hint: See §3.7 of the CVX users’ guide to find out how to retrieve optimal dual variables. To specify the quadratic objective, use quad_form(). (b) We will now solve some perturbed versions of the QP, with u1 = − 2 + δ1 , u2 = − 3 + δ2 , where δ1 and ...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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