Distributed databases are still very hard to keep safe because of the chance of hacking, unauthorized access, and data being different on different computers. Blockchain technology looks like a good idea because it uses immutability, digital proof, and consensus-driven verification to make sure that trust and resiliency are maintained. This article discusses about optimization methods, mathematical formulas, and game-theoretic models that are used in distributed environment for the efficient way performing data integrity and computing. By mixing blockchain with optimization tools, the study shows that attacks are less likely to succeed, risks are reduced, and data is securely stored.