Energy-Efficient Collaborative Task Computation Offloading in Cloud-Assisted Edge Computing for IoT Sensors

. 2019 Mar 4;19(5):1105. doi: 10.3390/s19051105

where	$M_{0} = [\begin{matrix} 0_{(4 K + 1) \times (4 K + 1)} & \frac{1}{2} b_{0} \\ \frac{1}{2} {(b_{0})}^{T} & 0 \end{matrix}]$ ,
	$M_{j} = [\begin{matrix} diag (e_{j}) & - \frac{1}{2} e_{j} \\ - \frac{1}{2} {(e_{j})}^{T} & 0 \end{matrix}]$ ,
	$M_{k}^{P} = [\begin{matrix} 0_{(4 K + 1) \times (4 K + 1)} & \frac{1}{2} b_{k}^{P} \\ \frac{1}{2} {(b_{k}^{P})}^{T} & 0 \end{matrix}]$ ,
	$M_{K}^{D} = [\begin{matrix} 0_{(4 K + 1) \times (4 K + 1)} & \frac{1}{2} b_{1} \\ \frac{1}{2} {(b_{1})}^{T} & 0 \end{matrix}]$ ,
	$M_{k}^{R} = [\begin{matrix} 0_{(4 K + 1) \times (4 K + 1)} & \frac{1}{2} e_{3 K + k} \\ \frac{1}{2} {(e_{3 K + k})}^{T} & 0 \end{matrix}]$ ,
	$M_{k j}^{R} = [\begin{matrix} 0_{4 K \times 4 K} & - \frac{1}{2} {[{(b_{2})}^{T} diag (b_{j}^{I})]}^{T} & \frac{1}{2} e_{3 K + k} \\ - \frac{1}{2} {(b_{2})}^{T} diag (b_{j}^{I}) & 0 & 0 \\ \frac{1}{2} {(e_{3 K + k})}^{T} & 0 & 0 \end{matrix}] .$