大规模有界约束优化中带非单调线搜索的子空间有限记忆BFGS方法

A Subspace Limited Memory BFGS Method with Nonmonotone Line Search for Large Scale Bound Constrained Problem

本文提出了一个大规模有界约束优化的积极集算法。积极集利用ε-近似技术识别。搜索方向有两部分构成:非积极变量所在空间的搜索方向采用有限记忆BFGS方法计算;另一部分通过一个显式计算。最后,在较弱条件下,证明了算法具有全局收敛性。

An active set algorithm for large scale bound constrained minimization is proposed in this paper.The active sets are estimated by an ε approximation identification technique.The search direction consists of two parts： in the subspace spanned by inactive variables,the search direction is defined by the limited memory BFGS method,the other part is defined by the subspace simple formulation.Finally,the global convergence is proved under mild condition.