Paper Info
Title
An Augmented Lagrangian Based Algorithm for Distributed NonConvex Optimization.
Abstract
This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interpreted as prices, a concept employed in dual decomposition methods and the alternating direction method of multipliers (ADMM). Here, each agent solves its own small-scale nonlinear programming problem and communicates with other agents by solving coupled quadratic programming problems. These coupled quadratic programming problems have equality constraints for which parallelizable methods are available. The use of techniques associated with standard sequential quadratic programming methods gives a method with superlinear or quadratic convergence rate under suitable conditions. This is in contrast to existing decomposition methods, such as ADMM, which have a linear convergence rate. It is shown how the proposed algorithm may be extended using globalization techniques that guarantee convergence to a local minimizer from any initial starting point.
Year
DOI
Venue
2016
10.1137/140975991
SIAM JOURNAL ON OPTIMIZATION
Keywords
Field
DocType
nonconvex optimization,large-scale problems,distributed algorithms
Parallelizable manifold,Discrete mathematics,Mathematical optimization,Quadratically constrained quadratic program,Active set method,Nonlinear programming,Algorithm,Augmented Lagrangian method,Quadratic programming,Sequential quadratic programming,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
26
2
1052-6234
Citations 
PageRank 
References 
10
0.54
0
Authors
3
Name
Order
Citations
PageRank
Boris Houska121426.14
Janick V. Frasch2373.00
Moritz Diehl31343134.37