Conservative Signal Processing Architectures For Asynchronous, Distributed Optimization Part I: General Framework

This paper presents a framework for designing a class of distributed, asynchronous optimization algorithms, realized as signal processing architectures utilizing various conservation principles. The architectures are specifically based on stationarity conditions pertaining to primal and dual variabl...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Baran, Thomas A, Lahlou, Tarek A
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 17.10.2014
Subjects:
Algorithms
Computer networks
Electrical networks
Optimization
Optimization algorithms
Signal processing
Superposition (mathematics)
ISSN:2331-8422
Online Access:Get full text
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Summary:This paper presents a framework for designing a class of distributed, asynchronous optimization algorithms, realized as signal processing architectures utilizing various conservation principles. The architectures are specifically based on stationarity conditions pertaining to primal and dual variables in a class of generally nonconvex optimization problems. The stationarity conditions, which are closely related to the principles of stationary content and co-content that can be derived using Tellegen's theorem in electrical networks, are in particular transformed via a linear change of coordinates to obtain a set of linear and nonlinear maps that form the basis for implementation. The resulting algorithms specifically operate by processing a linear superposition of primal and dual decision variables using the associated maps, coupled using synchronous or asynchronous delay elements to form a distributed system. A table is provided containing specific example elements that can be assembled to form various optimization algorithms directly from the corresponding problem statements.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1407.0418