Optimization algorithms play a crucial role in the process of handling enormous datasets in the age of big data. Traditional optimization methods often struggle with modern applications, sometimes taking days or even weeks to find a solution. My research program thus consists in developing and providing fast and resource-efficient, large-scale optimization methods to meet the demands of today's challenges. In this talk, I will highlight the increasing need for such methods and present two key approaches to address this demand: block decomposable and trust region methods. Both of these methods not only speed up solution time, sometimes reducing it from days to mere minutes or seconds, but also make it feasible to tackle problems that might previously be considered computationally intractable. Specifically, I will discuss Proximal ADMM, a block decomposable method, and an Inexact Proximal Trust Region Method, both of which offer efficient and scalable solutions to large-scale optimization challenges.