非凸优化中对于带不同惯性项的前后分裂算法的一种加速技术  

An Acceleration Technique of the Forward-backward Splitting Algorithm with Different Inertial Terms for Non-convex Optimization

作　　者：刘海玉 LIU Haiyu(Hebei University Of Technology,School of Science,Tianjin,300401 China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《科技创新导报》2021年第7期184-187,共4页Science and Technology Innovation Herald

摘　　要：本文考虑最小化一类非凸非光滑优化问题,对带不同惯性项的前后分裂算法中的步长作了改进,运用非单调线搜索技术来加快收敛速度。新算法利用了非单调线搜索技术,在每一次迭代中满足预先设置条件,从而在总体上使目标函数值有更大的下降。通过假设算法产生序列的有界性,本文利用数学归纳法完成了算法的序列收敛性证明。最后对非凸二次规划问题进行了数值实验,通过合适的参数选取,说明新算法有效地减少了迭代次数,达到预先给定的终止条件。In this paper,we consider minimizing a class of non-convex and non-smooth optimization problems,improve the step size of the forward-backward algorithm with different inertia terms,and use the nonmonotone proximal gradient technology to speed up the convergence.The new algorithm uses the nonmonotone proximal gradient technology to select the maximum value of adjacent objective functions in the iteration,so that the value of the function drops more.We prove the convergence of the new algorithm under strong hypothetical conditions.Finally,the numerical experiment is carried out on the non-convex quadratic programming problem,which proves that the new algorithm effectively improves the convergence speed of the original algorithm.

关 键 词：非凸优化 非单调线搜索技术 带不同惯性项的前后分裂算法 收敛速度 

分 类 号：O224[理学—运筹学与控制论]