bv_cvxbook_extra_exercises

Is f a convex function jointly in y b carefully

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Unformatted text preview: i−1 |/d |hi+1 − 3hi + 3hi−1 − hi−2 |/d 2 ≤D ≤D (2) , (3) , i = 2, . . . , n − 1 where D(1) is the maximum allowable road slope, D(2) is the maximum allowable curvature, and D(3) is the maximum allowable third derivative. (a) Explain how to find the optimal grading plan. (b) Find the optimal grading plan for the problem with data given in road_grading_data.m, and fill and cut cost functions φfill (u) = 2(u)2 + 30(u)+ , + φcut = 12(u)2 + (u)+ . + Plot hi − ei for the optimal grading plan and report the associated cost. (c) Suppose the optimal grading problem with n = 1000 can be solved on a particular machine (say, with one, or just a few, cores) in around one second. Assuming the author of the software took EE364a, about how long will it take to solve the optimal grading problem with n = 10000? Give a very brief justification of your answer, no more than a few sentences. 126 15 Graphs and networks 15.1 A hypergraph with nodes 1, . . . , m is a set of nonempty subsets of {1, 2, . . . , m}, called edges. An ordinary graph i...
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