bv_cvxbook_extra_exercises

We can think of ax b as a set of limits on m

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Unformatted text preview: 6 N = 30. You can do this by forming the LP you found in your solution of exercise 4.16, or more directly using CVX. Plot the actuator signal u(t) as a function of time t. 3.18 Heuristic suboptimal solution for Boolean LP. This exercise builds on exercises 4.15 and 5.13 in Convex Optimization, which involve the Boolean LP minimize cT x subject to Ax b xi ∈ {0, 1}, i = 1, . . . , n, with optimal value p⋆ . Let xrlx be a solution of the LP relaxation minimize cT x subject to Ax b 0 x 1, so L = cT xrlx is a lower bound on p⋆ . The relaxed solution xrlx can also be used to guess a Boolean point x, by rounding its entries, based on a threshold t ∈ [0, 1]: ˆ xi = ˆ 1 xrlx ≥ t i 0 otherwise, for i = 1, . . . , n. Evidently x is Boolean (i.e., has entries in {0, 1}). If it is feasible for the Boolean ˆ LP, i.e., if Ax b, then it can be considered a guess at a good, if not optimal, point for the Boolean ˆ LP. Its objective value, U = cT x, is an upper bound on p⋆ . If U and L are close, then x is nearly ˆ ˆ optimal; specifically, x cannot be mo...
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