求解非光滑问题的一种修正LS共轭梯度算法

A modified Liu-Storey conjugate gradient algorithm for nonsmooth minimization problems

针对非光滑无约束凸函数的极小化问题,提出改进的LS共轭梯度算法。其产生的搜索方向不仅具有充分下降性和信赖域的特点,而且算法在适当条件下具有全局收敛性。数值结果证明了该算法对于非光滑问题是有效的,从而改进的LS共轭梯度算法能够高效快捷地处理非光滑无约束凸函数的极小化问题。

A modified LS conjugate gradient algorithm is proposed for solving unconstrained nonsmooth convex minimization problems. The search direction has the characteristics of sufficient descent and trust region. The algorithm is globally convergent under mild conditions. The numerical results indicate that the proposed algorithm is effective for the given nonsmooth problems, and therefore the modified LS conjugate gradient algorithm can deal with unconstrained nonsmooth convex minimization problems efficiently.