On Coordinated Primal-Dual Interior-Point Methods for Multi-Agent Optimization

This paper presents a coordinated primal-dual interior point (PDIP) method for solving structured convex linear and quadratic programs (LP-QP) in a distributed man- ner. The considered class of problems represents a multi-agent setting, where the aggregated cost is to be minimized while respecting coupling constraints as well as local constraints of the agents. Unlike fully distributed methods, a central agent is utilized, which coordinates the Newton steps taken within the interior-point algorithm. In practical PDIP implementations, predictor-corrector variants are widely used, due to their very fast convergence. We show that in the coordinated case, a naive implementation of a PDIP with predictor-corrector scheme introduces extra communication steps between local and central agents. We propose a decentralized predictor-corrector scheme that uses a non-uniform perturbation on the complementary slackness condition, which is able to reduce the number of communication steps while preserving fast convergence of the original methods. We analyse the general framework of PDIP methods with non-uniform perturbations and provide convergence and complexity results, that directly apply to the proposed coordinated PDIP with decentralized predictor- corrector scheme

A new decomposition method applied to optimization problems arising in power systems: Local and global behavior

In this report a new decomposition methodology for optimization problems is presented. The proposed procedure is general, simple and efficient. It avoids most disadvantages of other common decomposition techniques, such as Lagrangian Relaxation or Augmented Lagrangian Relaxation. The new methodology is applied to a problem coming from interconnected power systems. The application of the new method to this problem allows the computation of an optimal coordinated but decentralized solution. Local and global convergence properties of the proposed decomposition algorithm are described. Numerical results show that the new decentralized methodology has a lower computational cost than other decomposition techniques, and in large-scale cases even lower than a centralized approach