C formulate the norm approximation problem minimize

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Unformatted text preview: onvex, and has units of kg/s. You are given the data d (segment travel distances), smin and smax (speed bounds), τ min and τ max (waypoint arrival time bounds), and the fuel use function Φ : R → R. You are to choose the speeds s1 , . . . , sn so as to minimize the total fuel consumed in kg. (a) Show how to pose this as a convex optimization problem. If you introduce new variables, or change variables, you must explain how to recover the optimal speeds from the solution of your problem. If convexity of the objective or any constraint function in your formulation is not obvious, explain why it is convex. (b) Carry out the method of part (a) on the problem instance with data in veh_speed_sched_data.m. Use the fuel use function Φ(si ) = as2 + bsi + c (the parameters a, i b, and c are defined in the data file). What is the optimal fuel consumption? Plot the optimal speed versus segment, using the matlab command stairs to better show constant speed over the segments. 3.21 Norm approximation via SOCP, fo...
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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 University of California, Berkeley.

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