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They satisfy the KKT optimality conditions of (36) for P. Therefore, according to the rate-WMMSE relationship (35) and the common rate transformation c=−x, problem (36) can be transformed to problem (15).
Then Problem 1 can be transformed to problem (1.1).
Therefore Problem P as stated above can be transformed to Problem Q.
Therefore, for a specific t, Problem P11 can be transformed to Problem P12 through introducing new variables T k : Problem P12 (for a specific t): max W k, P k S, P k R, T k R W k, P k S, P k R, T k = ∑ k = 1 K T k (42).
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Apparently, the Minimum-Delay POIs Coverage problem can be transformed to the problem of minimizing the maximal trajectory of mobile sensors: given k mobile sensors, find a set of k trajectories to pass all POIs such that the maximum length among all k trajectories is minimized.
In fact, the problem of covering a circle with random arcs can be transformed to the problem of covering a piece of line, say the interval, with random intervals.
It is well known that optimization problems can be transformed to the problems of the existence of a best proximity point.
The problem can be transformed to a knapsack problem and the optimal solution reaches a Walrasian equilibrium.
This problem can be transformed to a convex problem by recognizing that (P2) is invariant w.r.t. the absolute phase of f u.
Although problem (PNR) is nonconvex, it can be transformed to a convex problem and solved globally and efficiently[1 4].
Therefore almost all existence results for boundary value problems with state-dependent impulses have been reached for periodic problems which can be transformed to fixed point problems of corresponding Poincaré maps in R n.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com