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.

中文翻译：

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有界约束非光滑问题的有限内存BFGS子空间算法

子空间技术已被广泛用于解决无约束/有约束的优化问题，并且已经获得了许多结果。针对框约束条件下的大规模非光滑优化问题，提出了一种结合有限内存BFGS更新的子空间算法。该算法可以确保所有迭代点都是可行的，并且目标函数的序列在减少。而且，允许活动集中的快速变化。全局收敛是在某些合适的条件下建立的。数值结果表明，该方法对于大规模的非光滑盒约束优化非常有效，其中最大的测试问题是11,000个变量。