Local Projection and Global Tracking-Based Decentralized Optimization: Take Local Energy Trading as an Example

Optimization problems arise in various domains, ranging from power systems to resource allocation and large network management. An effective solution to these problems in a distributed manner has become a crucial research area due to the increasing scale and complexity of modern systems. In this article, we propose a novel local projection global tracking (LPGT) decentralized algorithm based on the Alternating Direction Method of Multipliers for general optimization problems. Unlike existing distributed methods that require problem-specific adaptations or centralized coordination, LPGT provides tailored solutions for handling generic local equality and inequality constraints, as well as global coupled equality and inequality constraints. Moreover, a projection-based analytical scheme is designed to handle generic local equality and inequality constraints without iterative subproblem solvers, and a fully decentralized deviation tracking mechanism is constructed to enforce both global coupled equalities and inequalities constraints via agent communications, eliminating the need for a central coordinator. Case studies for a local energy trading model are proposed to verify the feasibility and applicability of the algorithm.