Overlapping Schwarz Decomposition for Constrained Quadratic Programs

@article{Shin2020OverlappingSD,
  title={Overlapping Schwarz Decomposition for Constrained Quadratic Programs},
  author={Sungho Shin and Mihai Anitescu and Victor M. Zavala},
  journal={2020 59th IEEE Conference on Decision and Control (CDC)},
  year={2020},
  pages={3004-3009}
}
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have recently shown that they are also effective at solving structured optimization problems. In the proposed scheme, we consider QPs whose algebraic structure can be represented by graphs. The graph domain is partitioned into overlapping subdomains (yielding a set… 

Figures and Tables from this paper

Graph-Based Modeling and Decomposition of Energy Infrastructures
A Julia Framework for Graph-Structured Nonlinear Optimization
TLDR
This work presents a Julia framework for modeling and solving graph-structured nonlinear optimization problems and demonstrates the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.
Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs
TLDR
The results provide new insights on how perturbations propagate through the NLP graph and on how the problem formulation influences such propagation, and provide empirical evidence that positive objective curvature and constraint flexibility tend to dampen propagation.
A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl
TLDR
This work presents a general graph-based modeling abstraction for optimization that is called an OptiGraph, which enables the modular construction of highly complex models in an intuitive manner, facilitates the use of graph analysis tools, and facilitates communication of structures to decomposition algorithms.

References

SHOWING 1-10 OF 34 REFERENCES
Decentralized Schemes With Overlap for Solving Graph-Structured Optimization Problems
TLDR
The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs.
Diffusing-Horizon Model Predictive Control
We present a new time-coarsening strategy for model predictive control (MPC) that we call diffusing-horizon MPC. This strategy seeks to overcome the computational challenges associated with optimal
Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming
TLDR
Under uniform controllability and boundedness assumptions for the problem data, it is proved that the directional derivative of the optimal state and control at time k will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length.
Advanced-step multistage nonlinear model predictive control: Robustness and stability
The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms
TLDR
This IEEE PES Task Force report proposes a standardized AC-OPF mathematical formulation and the PGLib-OPf networks for benchmarking AC-opF algorithms and a motivating study demonstrates some limitations of the established network datasets in the context of benchmarking ASF algorithms.
A Hierarchical Optimization Architecture for Large-Scale Power Networks
TLDR
It is shown that state and dual information obtained from the top layer can be used to accelerate the coordination of the decentralized optimization agents and to recover optimality for the entire system.
Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control
TLDR
This work analyzes the sensitivity of the extremal equations that arise from the first order optimality conditions for time dependent optimization problems and considers parabolic PDEs.
Temporal Decomposition Scheme for Nonlinear Multisite Production Planning and Distribution Models
In this paper we propose a multiperiod nonlinear programming model for the production planning and product distribution of several continuous multiproduct plants that are located in different sites
Decomposition of Nonconvex Optimization via Bi-Level Distributed ALADIN
TLDR
This article proposes a framework for decentralized nonconvex optimization via bi-level distribution of the augmented Lagrangian alternating direction inexact Newton (ALADIN) algorithm and shows how decentralized variants of conjugate gradient and alternating direction of multipliers method (ADMM) can be employed at the inner level.
...
...