求解大规模非光滑优化问题的一种修正Hestenes-Stiefel共轭梯度算法

A Modified Hestenes-Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization Problems

利用Moreau-Yosida正则化技术和非单调线搜索技术,设计了一种针对大规模非光滑优化问题的修正Hestenes-Stiefel共轭梯度算法.该算法的搜索方向不仅自动满足充分下降条件,而且属于信赖域.在适当条件下,新算法全局收敛.初步的数值实验也表明新算法对于求解大规模非光滑无约束凸优化问题是有效的.

This paper gives a modified Hestenes-Stiefel conjugate gradient algorithm for large-scale nonsmooth optimization problems,using the Moreau-Yosida regulation approach in combination with the nonmonotone line search technique.The search direction of the algorithm not only possesses the sufficient descent property but also belongs to a trust region.The new algorithm has the global convergence under proper conditions.A preliminary numerical experiment shows that the algorithm proposed herein is more effective than the normal method for large-scale non-smooth unconstrained convex optimization problems.