求解非光滑优化问题的一种修正FR共轭梯度算法

A Three-term Conjugate Gradient Algorithm for Large-scale Nonsmooth Minimizations

为了提高求解大规模非光滑问题的效率,设计一种求解非光滑优化问题的修正的Fletcher-Reeves三项非线性共轭梯度算法.该算法使用一种新的搜索方向.并利用Moreau-Yosida正则化技术和Armijo-type线搜索技术进行设计.新算法具有以下特点:一是搜索方向自动满足充分下降条件,二是算法的搜索方向具有信赖域性质;三是在适当条件下,证明了新算法全局收敛.初步的数值实验也表明新算法在求解大规模非光滑优化问题方面比传统LMBM算法更有竞争力.因此新算法能够更加高效地求解大规模非光滑优化问题.

To improve the efficiency for large-scale nonsmooth problems,a modified threeterm Fletcher-Reeves conjugate gradient algorithm for nonsmooth optimization problems is proposed.In this algorithm,a new search direction is given,and the Moreau-Yosida regularization technique and the Armijo-type line search technique are used to design the algorithm.The new algorithm has the following properties:1)the sufficient descent condition is satisfied for this algorithm without any line search;2)the trust region is satisfied too;3)the global convergence of the new algorithm is proved under suitable conditions.The preliminary numerical experiments are reported to show that the new algorithm is more efficient than that of the LMBM method for large-scale nonsmooth unconstrained optimization problems.So the presented algorithm is efficiently used to solve large-scale nonsmooth optimization problems.