Abstract
This paper investigates the distributed convex optimization problem with coupled inequality constraints over unbalanced digraphs depicted as row-stochastic matrices, where each agent in the network only has access to its local information, while the local constraint functions of all the agents are coupled in inequality constraints. To solve this kind of problems, a novel distributed iterative algorithm is proposed via consensus scheme and the projected primal-dual subgradient method. Different from the previous related results, our algorithm can not only deal with coupling inequality constraints but also conquer the unbalanced topology caused by directed graphs. Moreover, it is proved that under certain assumptions, the optimal solution of the problem can be asymptotically obtained by performing the designed algorithm. Finally, the numerical examples are presented to further illustrate the efficacy of the proposed approach.
Highlights
During the last decade, distributed optimization has drawn growing research interest, owing to its theoretical significance and widespread application in different areas such as power grids [1], [2], sensor networks [3], social networks [4], robotics [5] and so on
To cope with this issue, discrete-time [9], [10] and continuous-time [11], [12] distributed algorithms have been proposed to solve the problem with a coupled equality constraint, under the assumption that the coupled constraint is satisfied at the initial points
It is worth noting that the approaches proposed in [1], [9]–[13] are only suitable for solving the problems with coupled equality constraints, but they may fail to address the ones with coupled inequality constraints
Summary
During the last decade, distributed optimization has drawn growing research interest, owing to its theoretical significance and widespread application in different areas such as power grids [1], [2], sensor networks [3], social networks [4], robotics [5] and so on. Based on the dual decomposition method, a distributed dual subgradient iterative strategy is proposed in [14], which can solve the problem with coupled inequality constraints over weight-balanced digraphs. In [15], a consensus-based distributed primal-dual perturbation strategy has been presented and analyzed, where the average consensus method is adopted to estimate the global objective function and constraint function over weight-balanced digraphs. (a) The distributed primal-dual iterative algorithm proposed in this paper is capable of solving the problem with coupled inequality constraints which may be nonlinear, while the results in [1], [9]–[13] are only able to cope with linear coupled equality constraints and are invalid for our set-up. Let xi and [M ]ij respectively denote the ith entry of a vector x and the (i, j)th entry of a matrix M
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