An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints

It is well known that the active set algorithm is very effective for smooth box constrained optimization. Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective function smooth. A limited memory BFGS method is introduced to decrease the workload of the computer. The presented algorithm has these properties: (1) all iterates are feasible and the sequence of objective functions is decreasing; (2) rapid changes in the active set are allowed; (3) the subproblem is a lower dimensional system of linear equations. The global convergence of the new method is established under suitable conditions and numerical results show that the method is effective for large-scale nonsmooth problems (5,000 variables).