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arXiv · 1904.01196

Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization

Sulaiman A. Alghunaim·Ali H. Sayed
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Abstract

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear (exponential) convergence of the algorithm for smooth strongly-convex cost functions and study its relation to the non-incremental implementation. We also study the effect of the augmented Lagrangian penalty term on the performance of distributed optimization algorithms for the minimization of aggregate cost functions over multi-agent networks.

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Sulaiman A. Alghunaim, Ali H. Sayed. 2019-04-02. Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization. https://arxiv.org/abs/1904.01196

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