An Augmented Lagrangian Method for l2,1-Norm Minimization Problems in Machine Learning

In the fields of computer version, text classification and biomedical informatics, it needs to find the joint feature among serval learning tasks. Generally, resent results show that it can be realized by solving a ℓ_2,1-norm minimization problem. However, due to the non-smoothness of the norm, solving the resulting optimization problem is always challenging. This thesis designs an augmented Lagrange function method which is used to solve ℓ_2,1-norm minimization problem. In this thesis the convergence property of the algorithm is discussed. The numerical experiments indicate that the convergence of this algorithm is easily followed and the algorithm´s executing efficiency is very good.