bv_cvxbook_extra_exercises

153 utility versus latency trade o in a network we

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Unformatted text preview: for the problem instance with data σ = 1, 0.3 −0.1 −0.9 0.3 −0.3 . G = −0.6 −0.3 0.6 0.2 Give an optimal F , and the associated optimal objective value. 14.10 Fuel use as function of distance and speed. A vehicle uses fuel at a rate f (s), which is a function of the vehicle speed s. We assume that f : R → R is a positive increasing convex function, with dom f = R+ . The physical units of s are m/s (meters per second), and the physical units of f (s) are kg/s (kilograms per second). (a) Let g (d, t) be the total fuel used (in kg) when the vehicle moves a distance d ≥ 0 (in meters) in time t > 0 (in seconds) at a constant speed. Show that g is convex. 124 (b) Let h(d) be the minimum fuel used (in kg) to move a distance d (in m) at a constant speed s (in m/s). Show that h is convex. 14.11 Minimum time speed profile along a road. A vehicle of mass m > 0 moves along a road in R3 , which is piecewise linear with given knot points p1 , . . . , pN +1 ∈ R3 , starting at p1 and ending at...
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