Continuous-time Distributed Heavy-ball Algorithm for Distributed Convex Optimization over Undirected

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This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization prob-lem by utilizing the gradient tracking strategy,with convergence acceleration being achieved.Both the undirected and unbalanced dir-ected graphs are considered,extending existing algorithms that primarily focus on undirected or balanced directed graphs.Our al-gorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided.Further-more,the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper.Finally,two numerical examples are presented to show the convergence performance of our algorithms.
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