This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where ...
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This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where all involved functions are not necessarily differentiable, only assumed to be convex. In order to solve this problem, a modified primal-dual continuous-time algorithm is proposed by projections on local feasible sets. With the aid of constructing a proper Lyapunov function candidate, the existence of solutions of the algorithm in the Caratheodory sense and the convergence of the algorithm to an optimal solution for the distributed optimization problem are established. Additionally, a sufficient condition is provided for making the algorithm fully distributed. Finally, the theoretical result is corroborated by a simulation example.
In this article, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the ...
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In this article, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the proposed algorithm can be decomposed into a group of individual input feedforward passive (IFP) systems that interact with each other using output feedback information. Based on this IFP framework, convergence conditions of a suitable coupling gain are derived over weight-balanced and uniformly jointly strongly connected topologies. It is also shown that the IFP-based algorithm converges exponentially when the topology is strongly connected. Second, a novel distributed derivative feedback algorithm is proposed based on the passivation of IFP systems. While most works on directed topologies require knowledge of eigenvalues of the graph Laplacian, the derivative feedback algorithm is fully distributed, namely, it is robust against randomly changing weight-balanced digraphs with any positive coupling gain and without knowing any global information. Finally, numerical examples are presented to illustrate the proposed distributed algorithms.
In this study, the authors design distributed algorithms for solving the Sylvester equation AX+XB=C in the sense of least squares over a multi-agent network. In the problem setup, every agent in the interconnected sys...
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In this study, the authors design distributed algorithms for solving the Sylvester equation AX+XB=C in the sense of least squares over a multi-agent network. In the problem setup, every agent in the interconnected system only has local information of some columns or rows of data matrices A, B and C, and exchanges information among neighbour agents. They propose algorithms with mainly focusing on a specific partition case, whose designs can be easily generalised to other partitions. Three distributed continuous-time algorithms aim at two cases for seeking a least-squares/regularisation solution from the viewpoint of optimisation. Due to the equivalence between an equilibrium point of each system under discussion and an optimal solution to the corresponding optimisation problem, the authors make use of semi-stability theory and methods in convex optimisation to prove convergence theorems of proposed algorithms that arrive at a least-squares/regularisation solution.
For the distributed optimization, a continuous-time algorithm in the form of a differential inclusion is established. In the considered communication topology, the first-order neighbors and the second-order neighbors ...
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ISBN:
(纸本)9789881563972
For the distributed optimization, a continuous-time algorithm in the form of a differential inclusion is established. In the considered communication topology, the first-order neighbors and the second-order neighbors of each agent can exchange information. Moreover, the optimal solution can be obtained by analysis the algorithm and different from the previous algorithms, the proposed algorithm can solve the distributed optimization in directed case. Finally, a numerical example is given.
For the distributed optimization, a continuous-time algorithm in the form of a differential inclusion is established. In the considered communication topology, the first-order neighbors and the second-order neighbors ...
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For the distributed optimization, a continuous-time algorithm in the form of a differential inclusion is established. In the considered communication topology, the first-order neighbors and the second-order neighbors of each agent can exchange information. Moreover, the optimal solution can be obtained by analysis the algorithm and different from the previous algorithms,the proposed algorithm can solve the distributed optimization in directed case. Finally, a numerical example is given.
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in whi...
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This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the constrained optimization problem. Then we prove that all the agents of the algorithm can find the same optimal solution, and meanwhile, keep the states bounded while seeking the optimal solutions. We conduct a complete convergence analysis by employing nonsmooth Lyapunov functions for the stability analysis of differential inclusions. Finally, we provide a numerical example for illustration.
We give a new analysis of a class of continuous-time subspace tracking algorithms, related to a number of discrete-timealgorithms, such as stochastic gradient algorithms, spherical subspace trackers, and a new discre...
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We give a new analysis of a class of continuous-time subspace tracking algorithms, related to a number of discrete-timealgorithms, such as stochastic gradient algorithms, spherical subspace trackers, and a new discrete-time algorithm based on one of the continuous-time algorithms. Using formulas for tracking the singular value decomposition (SVD) of a time-varying matrix, we show attraction to orthogonality of the matrix representing the subspace estimate, and we analyze the evolution of the canonical angles between the subspace estimate and the subspace to be estimated.
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