求解非光滑优化问题的修正HS三项共轭梯度法

为了提高大规模非光滑优化问题的求解效率,克服其他方法存储需求大、算法复杂等缺点,提出求解非光滑优化问题的一种修正HS共轭梯度算法。在经典HS三项共轭梯度法的基础上提出一种新的搜索方向,并利用Moreau-Yosida正则化技术和Armijo-type线搜索技术进行设计。新算法满足充分下降条件,搜索方向属于信赖域,在适当条件下证明了新算法全局收敛。初步的数值实验表明新算法在求解非光滑无约束优化问题方面比LMBM方法更有效。新算法不仅具有较好的收敛性质,而且数值表现良好,为更加高效地求解非光滑优化问题提供了新的方法。

A modified three-term HS conjugate gradient method for solving nonsmooth minimizations

To improve the efficiency for large-scale nonsmooth optimization problems and overcome the large storage requirements and complex computation of other algorithms, a modified HS conjugate gradient algorithm for nonsmooth optimization problems is proposed. A new search direction based on the classical HS conjugate gradient method is given, then the Moreau-Yosida regularization technique and the Armijo-type line search technique are used to design the algorithm. The sufficient descent condition and the trust region are satisfied for this algorithm. Under suitable conditions, the global convergence of the new algorithm is proved. The preliminary numerical experiments show that the new algorithm is more efficient than the LMBM method for nonsmooth unconstrained optimization problems. The presented algorithm is efficiently for solving nonsmooth optimization problems since it has good convergence property and good numerical performance.