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The subspace technique has been widely used to solve unconstrained/constrained optimization problems and there exist many results that have been obtained. In this paper, a subspace algorithm combining with limited memory BFGS update is proposed for large-scale nonsmooth optimization problems with box-constrained conditions. This algorithm can ensure that all iteration points are feasible and the sequence of objective functions is decreasing. Moreover, rapid changes in the active set are allowed. The global convergence is established under some suitable conditions. Numerical results show that this method is very effective for large-scale nonsmooth box-constrained optimization, where the largest dimension of the test problems is 11,000 variables.

A limited memory BFGS subspace algorithm for bound constrained nonsmooth problems