A study on augmented Lagrangian-based splitting methods for separable convex programming - Wang, Kai (2017)
Convex programming has played an important role in studying a wide class of applications arising from computer science, statistics, industrial engineering, and management. Moreover, the advent of big-data analytics has resulted in very large-scale structural convex programming problems, thereby necessitating the research towards devising fast numerical algorithms for solving such problems. The goal of this thesis is to propose some efficient augmented Lagrangian-based splitting methods for solving the convex programming problem, provide an in-depth study of the convergence and convergence rate properties of these algorithms, and discuss computational results that establish the efficiency of these methods.