DESIGN AND OPTIMIZATION OF ALGORITHMS FOR LARGE-SCALE DATA ANALYSIS

A well-known way of solving difficult constrained problems is the augmented Lagrangian method (ALM). It takes on difficult optimisation issues by decomposing them into a series of comparatively smaller subproblems, many of which are not limited by the original variable. Dual variables are used into the ALM technique to ensure that constraints are satisfied during the optimisation process. When it comes to resolving the subproblems connected to the primal variable, ALM gives a great degree of flexibility. Due to this adaptability, a wide variety of primal-dual approaches based on ALM have emerged. These techniques effectively handle diverse large-scale and distributed applications by utilising the power of ALM. When dealing with inexact updates, our main focus is on providing accurate complexity results that take computation and communication costs into account. We also want to propose and evaluate the best techniques for distributed consensus efficiency. Here, we provide an overview of the augmented Lagrangian method (ALM) and its variants, which are designed to address convex optimised issues in large-scale and distributed contexts. We use control-theoretic tools in the analysis and design of these algorithms to make them easier to comprehend. We not only review recent developments in this area but also provide fresh perspectives on two novel applications, distributed energy trading and federated learning. In order to deal with inexact updates, our method focuses on achieving precise complexity results that take computational and communication expenses into account. Additionally, we concentrate on creating and evaluating the best techniques for distributed consensus optimisation. We explain ALM and its modifications in a tutorial-style presentation, highlighting its effectiveness in resolving convex optimisation issues in large-scale and dispersed contexts. We study the use of these strategies in the contexts of federated education and distributed trading of energy while using control-theoretic instruments for analysis and design