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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
0.2 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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- Fall '13
- The Aeneid