bv_cvxbook_extra_exercises

The process latencies depend on the process load and

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Unformatted text preview: s of the objects, but this won’t matter here.) We will select our ranking r as a minimizer of the total preference violation penalty, defined as m φ ( v (k ) ) , J= k=1 where v (k) is the preference violation of (i(k) , j (k) ) with r, and φ is a nondecreasing convex penalty function that satisfies φ(u) = 0 for u ≤ 0. (a) Make a (simple, please) suggestion for φ for each of the following two situations: (i) We don’t mind some small violations, but we really want to avoid large violations. (ii) We want as many preferences as possible to be consistent with the ranking, but will accept some (hopefully, few) larger preference violations. (b) Find the rankings obtained using the penalty functions proposed in part (a), on the data set found in rank_aggr_data.m. Plot a histogram of preference violations for each case and briefly comment on the differences between them. Give the number of positive preference violations for each case. (Use sum(v>0.001) to determine this number.) 149 Remark. The objects could be candidates for a position, papers at a conference, movies, we...
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