DeepAI AI Chat
Log In Sign Up

Scalable Primal Decomposition Schemes for Large-Scale Infrastructure Networks

by   Alexander Engelmann, et al.
University of Wisconsin-Madison
Argonne National Laboratory

The real-time operation of large-scale infrastructure networks requires scalable optimization capabilities. Decomposition schemes can help achieve scalability; classical decomposition approaches such as the alternating direction method of multipliers (ADMM) and distributed Newtons schemes, however, often either suffer from slow convergence or might require high degrees of communication. In this work, we present new primal decomposition schemes for solving large-scale, strongly convex QPs. These approaches have global convergence guarantees and require limited communication. We benchmark their performance against the off-the-shelf interior-point method Ipopt and against ADMM on infrastructure networks that contain up to 300,000 decision variables and constraints. Overall, we find that the proposed approaches solve problems as fast as Ipopt but with reduced communication. Moreover, we find that the proposed schemes achieve higher accuracy than ADMM approaches.


page 1

page 2

page 3

page 4


A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization

In this paper, we propose an algorithmic framework dubbed inertial alter...

Asynchronous ADMM for Distributed Non-Convex Optimization in Power Systems

Large scale, non-convex optimization problems arising in many complex ne...

Bethe-ADMM for Tree Decomposition based Parallel MAP Inference

We consider the problem of maximum a posteriori (MAP) inference in discr...

SnapVX: A Network-Based Convex Optimization Solver

SnapVX is a high-performance Python solver for convex optimization probl...

Two-block vs. Multi-block ADMM: An empirical evaluation of convergence

Alternating Direction Method of Multipliers (ADMM) has become a widely u...

On the Convergence of the Dynamic Inner PCA Algorithm

Dynamic inner principal component analysis (DiPCA) is a powerful method ...

Solving Constrained Variational Inequalities via an Interior Point Method

We develop an interior-point approach to solve constrained variational i...