Distributed computing faces a persistent multi agent trust dilemma. In the computation process, participants may maliciously attack the system for personal gain by providing false data. Blockchain provides a possible solution for this problem with its immutability and multi-party consensus. However, existing blockchain data throughput has long been queried owing to its exorbitant time and energy costs by consensus mechanisms. This paper proposes a light blockchain structure in distributed computing scenarios. A No-Proof consensus (NPC) mechanism is designed for distributed computing problems with no extra proving process such as Proof-of-Work or Proof-of-Stake. This consensus mechanism notices that the distributed computing result has proven to be valid in the computation process automatically, which does not need to be verified again in the consensus mechanism. Further, the single-threaded data processing ability of the blockchain structure certainly leads to low efficiency when applied to distributed computation problems. An NPC-based blockchain is constructed in this paper to solve this problem. In this structure, the distributed computing is done off chain, and an oracle is designed to upload the computing results to the blockchain asynchronously. Upon the contribution in this paper, a distributed energy trading model is provided as a case study to verify the superiority of the designed blockchain in contrast with other similar structures.

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.