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

TL;DR

This paper introduces a general framework for designing distributed, asynchronous optimization algorithms using signal processing architectures based on conservation principles and stationarity conditions, applicable to nonconvex problems.

Contribution

It proposes a novel signal processing architecture framework for asynchronous distributed optimization grounded in conservation principles and stationarity conditions.

Findings

Framework enables design of distributed asynchronous algorithms

Uses conservation principles related to Tellegen's theorem

Provides example elements for algorithm assembly

Abstract

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.