一类凸优化的加速混合下降算法

发布时间：2018-05-16 17:30

本文选题：凸优化问题 + 混合下降算法　；参考：《计算数学》2017年02期

【摘要】：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.
[Abstract]:A set of descent directions is obtained by using the known information of the approximate condition and the random number expansion prediction correction step in the hybrid descent algorithm for convex optimization problems. The forward acceleration shrinkage algorithm uses the technology of the Gao Si Seydel iteration algorithm and combines the idea of the adjacent point algorithm and the approximate adjacent point algorithm to construct the expansive descent direction. Based on the idea of hybrid descent algorithm and forward acceleration shrinkage algorithm, this paper improves the descent direction of hybrid descent algorithm by using the information of approximate rules, and obtains an accelerated hybrid descent algorithm for a class of convex optimization problems. Then the probabilistic convergence of the algorithm is proved by using the Markov inequality, the properties of convex functions and the basic properties of projection. A series of numerical experiments show the effectiveness and efficiency of the accelerated hybrid descent algorithm.
【作者单位】：中国民用航空飞行学院计算机学院;南京审计大学理学院;
【基金】：国家自然科学基金(U1233105)资助项目
【分类号】：O224

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