bv_cvxbook_extra_exercises

The total utility which we want to maximize is n u j

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Unformatted text preview: 2 6 3 In this example, tasks 1, 2, and 5 start at time t = 0 (since they have no precedents). Task 1 finishes at t = τ1 , task 2 finishes at t = τ2 , and task 5 finishes at t = τ5 . Task 3 has tasks 1 and 2 as precedents, so it starts at time t = max{τ1 , τ2 }, and ends τ3 seconds later, at t = max{τ1 , τ2 } + τ3 . Task 4 completes at time t = τ1 + τ4 . Task 6 starts when tasks 3, 4, and 5 have finished, at time t = max{max{τ1 , τ2 } + τ3 , τ1 + τ4 , τ5 }. It finishes τ6 seconds later. In this example, task 6 is the last task to be completed, so we have T = max{max{τ1 , τ2 } + τ3 , τ1 + τ4 , τ5 } + τ6 . (a) Formulate the problem of choosing processor speeds (between the given limits) to minimize completion time T , subject to an energy limit E ≤ Emax , as a convex optimization problem. 139 The data in this problem are P , smin , smax , α1 , . . . , αn , Emax , and the function f . The variables are s1 , . . . , sn . Feel free to change variables or to introduce new variables. Be sure to explain clearly why your...
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