• 论文 •

### 一类凸优化的加速混合下降算法

1. 1. 中国民用航空飞行学院 计算机学院, 广汉 618307;
2. 南京审计大学 理学院, 南京 211815
• 收稿日期:2016-06-28 出版日期:2017-05-15 发布日期:2017-07-18
• 基金资助:

国家自然科学基金（U1233105）资助项目.

Xu Haiwen, Sun Liming. A ACCELERATED HYBRID DESCENT ALGORITHM FOR CONVEX MINIMIZATION[J]. Mathematica Numerica Sinica, 2017, 39(2): 200-212.

### A ACCELERATED HYBRID DESCENT ALGORITHM FOR CONVEX MINIMIZATION

Xu Haiwen1, Sun Liming2

1. 1. College of Computer Science and Technology, Civil Aviation Flight University of China, Guanghan 618307, China;
2. College of Science, Nanjing Audit University, Nanjing 211815, China
• Received:2016-06-28 Online:2017-05-15 Published:2017-07-18

The set of descent directions of hybrid descent method (HD Method) for convex minimization is obtained by the known information of approximate conditions and random number expansion prediction correction step.While the rich expansion descent directions of forward accelerated contraction method is constructed by the technology of Gauss-Seidel iterative algorithm and the thoughts of proximal point algorithm (PPA) and approximate proximal point algorithm.Inspired by the idea of the hybrid descent algorithm and the forward acceleration algorithm,the accelerated hybrid descent algorithm for convex minimization is obtained by using the history approximate rule information to improve the iterative step of hybrid descent algorithm.Subsequetly,the probability convergence of accelerated hybrid descent algorithm is introduced by the basic properties of Markov's inequality,the convex function and the projection.Some numerical experiments show the effectiveness and efficiency of the accelerated hybrid descent algorithm.

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