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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