Generalized LASSO Problem with Equality and Inequality Constraints Using ADMM

Abstract

With the development of technology, the volume of the data has gradually become much larger and attracting much more attention in data science. Statisticians nowadays need to consider the case when the dataset is extremely huge, which can be referred to as "Big Data Problem". In the applications of big data analysis, many problems can be formulated into the family of convex optimization problem. In my dissertation, I will mainly discuss the algorithm of alternating direction of multipliers method (ADMM), which is an efficient algorithm in distributed convex optimization and attracting more and more attention in recent years because of its superior performance in big data analysis and machine learning. This algorithm is generally useful in splitting the global problem into subproblems and solving the parallel computing of those subproblems instead of working on the global problem directly. Generalized LASSO problem is one of the most commonly used convex optimization problems. In this dissertation, I will focus on the generalized LASSO problem with equality and inequality constraints. Several ADMM and distributed ADMM algorithms will be proposed to solve the problem with high efficiency and low computational cost.