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arXiv · 1510.08580

Primal-Dual Algorithm for Distributed Constrained Optimization

Jinlong Lei·Han-Fu Chen·Hai-Tao Fang
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Abstract

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraint sets assigned to the agents. Based on the augmented Lagrange method, a distributed primal-dual algorithm with a projection operation included is proposed to solve the problem. It is shown that with appropriately chosen constant step size, the local estimates derived at all agents asymptotically reach a consensus at an optimal solution. In addition, the value of the cost function at the time-averaged estimate converges with rate $O(\frac{1}{k})$ to the optimal value for the unconstrained problem. By these properties the proposed primal-dual algorithm is distinguished from the existing algorithms for distributed constrained optimization. The theoretical analysis is justified by numerical simulations.

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Jinlong Lei, Han-Fu Chen, Hai-Tao Fang. 2016-03-06. Primal-Dual Algorithm for Distributed Constrained Optimization. https://arxiv.org/abs/1510.08580

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