Abstract
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.
Highlights
Consider the following large-scale nonsmooth optimization problems: min f (x), s.t. l ≤ x ≤ u, (1.1)where f (x) : n → is supposed to be locally Lipschitz continuous and the number of variables n is supposed to be large
The active sets are based on guessing technique to be identified at each iteration, the search direction in free subspace is determined by limited memory BFGS algorithm, which will provide an efficient means for attacking large-scale nonsmooth bound constrained optimization problems
♣ the nonsmooth objective function is descent; ♣ a limited memory BFGS method is given for nonsmooth problem; the iteration sequence {xk} is feasible; ♣ the global convergence of the new method is established; ♣ large-scale nonsmooth problems (11,000 variables) are successfully solved
Summary
Consider the following large-scale nonsmooth optimization problems: min f (x), s.t. l ≤ x ≤ u, (1.1)where f (x) : n → is supposed to be locally Lipschitz continuous and the number of variables n is supposed to be large. 1 Introduction Consider the following large-scale nonsmooth optimization problems: min f (x), s.t. l ≤ x ≤ u, (1.1)
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