徐海文¹, 孙黎明²

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.

A ACCELERATED HYBRID DESCENT ALGORITHM FOR CONVEX MINIMIZATION

Xu Haiwen¹, Sun Liming²

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:2016-06-28Online:2017-05-15Published:2017-07-18







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凸优化问题的混合下降算法利用近似条件的已知信息和随机数扩张预测校正步得到了一组下降方向.而前向加速收缩算法利用高斯赛德尔迭代算法的技术，结合邻近点算法和近似邻近点算法的思想，构造了富有扩张性的下降方向.本文借鉴混合下降算法和前向加速收缩算法的思想，利用已有近似规则信息改善了混合下降算法的下降方向，得到了一类凸优化问题的加速混合下降算法.随后利用\Markov不等式、凸函数性质和投影的基本性质等，实现了算法的依概率收敛证明.一系列数值试验表明了加速混合下降算法的有效性和效率性.
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