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Table 1 Different alternatives of Algorithm 1

From: Performance evaluation and analysis of distributed multi-agent optimization algorithms with sparsified directed communication

Method Type \(M_{i}^{k}\) \(\xi _{i,j}^{k}\) pk Relevant reference
FBI First order I \(z_{i}^{k} \cdot z_{j}^{k}\) pk=1−0.5k [12]
FBD First order I \(z_{i}^{k} \cdot z_{j}^{k}\) pk=(k+1)−1 [13]
FUI First order I \(z_{j}^{k}\) pk=1−0.5k this paper
FUD First order I \(z_{j}^{k}\) pk=(k+1)−1 [14]
FBC First order I 1 1 [15]
SBC Second order \(D_{i}^{k}\) 1 1 [5]
SBI Second order \(D_{i}^{k}\) \(z_{i}^{k} \cdot z_{j}^{k}\) pk=1−0.5k [16]
SBD Second order \(D_{i}^{k}\) \(z_{i}^{k} \cdot z_{j}^{k}\) pk=(k+1)−1 [13, 16]
SUI Second order \(D_{i}^{k}\) \(z_{j}^{k}\) pk=1−0.5k this paper
SUD Second order \(D_{i}^{k}\) \(z_{j}^{k}\) pk=(k+1)−1 this paper