This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Bot...
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This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, 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.
distributed joint congestion control and routing optimization has received a significant amount of attention recently. To date, however, most of the existing schemes follow a key idea called the back-pressure algorith...
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distributed joint congestion control and routing optimization has received a significant amount of attention recently. To date, however, most of the existing schemes follow a key idea called the back-pressure algorithm. Despite having many salient features, the first-order subgradient nature of the back-pressure based schemes results in slow convergence and poor delay performance. To overcome these limitations, in this paper, we make a first attempt at developing a second-order joint congestion control and routing optimization framework that offers utility-optimality, queue-stability, fast convergence, and low delay. Our contributions in this paper are three-fold: i) we propose a new second-order joint congestion control and routing framework based on a primal-dual interior-point approach;ii) we establish utility-optimality and queue-stability of the proposed second-order method;and iii) we show how to implement the proposed second-order method in a distributed fashion.
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