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Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over

Liping Feng1, Liang Ran2, Guoyang Meng3

  • 1Department of Computer Science, Xinzhou Teachers University, Xinzhou 034000, China.

Entropy (Basel, Switzerland)
|September 23, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a decentralized algorithm for solving complex optimization problems across networks. The method effectively handles nonsmooth composite problems using proximal operators without global parameters, ensuring efficient network-wide solutions.

Keywords:
decentralized optimizationdistributed signal processinginformation processingnonsmooth optimizationprimal-dual algorithmuncoordinated stepsizes

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Area of Science:

  • Optimization Theory
  • Network Science
  • Decentralized Systems

Background:

  • Nonsmooth composite optimization problems present significant challenges in decentralized network settings.
  • Existing methods often require global parameters or centralized coordination, limiting scalability.

Purpose of the Study:

  • To develop a decentralized algorithm for nonsmooth composite optimization problems over networks.
  • To address problems with both equality and box constraints.
  • To enable decentralized solutions without reliance on global parameters.

Main Methods:

  • Formulation of the problem using Lagrange functions to derive first-order optimal conditions.
  • Proposal of a decentralized algorithm incorporating proximal operators.
  • Convergence analysis utilizing fixed-point theory and operator-based algorithm representation.

Main Results:

  • A novel decentralized algorithm capable of handling nonsmooth composite optimization with constraints.
  • The algorithm features uncoordinated step-sizes, eliminating the need for global parameters.
  • Simulations using constrained quadratic programming problems validate the algorithm's effectiveness.

Conclusions:

  • The proposed decentralized proximal algorithm offers an effective solution for network-based nonsmooth composite optimization.
  • The method's ability to operate without global parameters enhances its applicability in distributed systems.
  • The convergence analysis provides theoretical guarantees for the algorithm's performance.