bv_cvxbook_extra_exercises

# B we will now solve some perturbed versions of the qp

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Unformatted text preview: ition. We will choose x0 and K in order to minimize the expected value of the objective, while insisting that for any value of u, feasibility is maintained: minimize E cT xaﬀ (u) subject to Axaﬀ (u) b(u) ∀u ∈ U . The variables here are x0 and K . The expectation in the objective is over u, and the constraint requires that Axaﬀ (u) b(u) hold almost surely. 24 (a) Explain how to ﬁnd optimal values of x0 and K by solving a standard explicit convex optimization problem (i.e., one that does not involve an expectation or an inﬁnite number of constraints, as the one above does.) The numbers of variables or constraints in your formulation should not grow exponentially with the problem dimensions n, p, or m. (b) Carry out your method on the data given in affine_pol_data.m. To evaluate your aﬃne policy, generate 100 independent samples of u, and for each value, compute the objective value of the aﬃne policy, cT xaﬀ (u), and of the optimal policy, cT x⋆ (u). Scatter plot the objective value of the aﬃne policy (y -axis) versus the objective value...
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