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end{aligned} Hence, (J_{varepsilon } u^{0}_{varepsilon },y^{0}_{varepsilon })<+infty) (which implies ((u^{0}_{varepsilon },y^{0}_{varepsilon })inXi_{Delta})) and ((u^{0}_{varepsilon },y^{0}_{varepsilon })) is an optimal pair to the corresponding optimization problem (4.1).

Then, a joint optimization iterative algorithm is proposed to search the optimal pair of sensing and transmission durations.

Pontryagin's maximum principle for the optimal pair.

Let ( y ¯ , u ¯ be an optimal pair.

Finally, the optimal pair of parameters is selected.

We call it an optimal pair of Problem ( C x ).

Proof of Theorem 1.1 I. Existence of optimal pair.

Let us know characterize the optimal pair of prices for both situations.

Then the Bolza problem (P) admits at least one optimal pair on (C I,mathbb{X} times U_{ad}).

The simulation determines the optimal pair of filters from among 265 filters for a given camera setup.

Then, the dual function can be easily found by searching the optimal pair (k, l) that maximizes the dual function.