bv_cvxbook_extra_exercises

However we do have matrix upper 26 bounds on the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online