Conservative Signal Processing Architectures For Asynchronous, Distributed Optimization Part II: Example Systems

TL;DR

This paper demonstrates how to design synchronous and asynchronous signal processing systems for various optimization problems using a unified framework, with examples including LASSO, SVM training, and filter design.

Contribution

It provides concrete examples of optimization algorithms based on a previous theoretical framework, illustrating their application to diverse problems and comparing different algorithmic approaches.

Findings

Algorithms successfully solve optimization problems with convergence discussed.

Multiple algorithms for the same problem demonstrate framework flexibility.

Numerical simulations validate the effectiveness of the proposed systems.

Abstract

This paper provides examples of various synchronous and asynchronous signal processing systems for performing optimization, utilizing the framework and elements developed in a preceding paper. The general strategy in that paper was to perform a linear transformation of stationarity conditions applicable to a class of convex and nonconvex optimization problems, resulting in algorithms that operate on a linear superposition of the associated primal and dual decision variables. The examples in this paper address various specific optimization problems including the LASSO problem, minimax-optimal filter design, the decentralized training of a support vector machine classifier, and sparse filter design for acoustic equalization. Where appropriate, multiple algorithms for solving the same optimization problem are presented, illustrating the use of the underlying framework in designing a variety of distinct classes of algorithms. The examples are accompanied by numerical simulation and a discussion of convergence.