bv_cvxbook_extra_exercises

179 resource allocation in stream processing a large

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Unformatted text preview: ×m , with Acontr = ij 1 i ∈ Aj 0 otherwise, contr Ttj = 1 t ∈ Tj 0 otherwise. Report the optimal net profit, and the associated revenue and total penalty payment. Give the same three numbers for the strategy of simply displaying in each period only the ad with the largest revenue per impression. 17.5 Ranking by aggregating preferences. We have n objects, labeled 1, . . . , n. Our goal is to assign a real valued rank ri to the objects. A preference is an ordered pair (i, j ), meaning that object i is preferred over object j . The ranking r ∈ Rn and preference (i, j ) are consistent if ri ≥ rj + 1. (This sets the scale of the ranking: a gap of one in ranking is the threshold for preferring one item over another.) We define the preference violation of preference (i, j ) with ranking r ∈ Rn as v = (rj + 1 − ri )+ = max{rj + 1 − ri , 0}. We have a set of m preferences among the objects, (i(1) , j (1) ), . . . , (i(m) , j (m) ). (These may come from several different evaluator...
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