| 摘要本文提出了求解单调包含问题的一类新的惯性混合非精确邻近点算法（简记为iHIPPA）.在适当的参数假设下，我们证明了求解单调包含问题的iHIPPA所产生点列的弱收敛性，获得了iHIPPA的非渐近收敛率为O（1/√k）及iHIPPA的遍历迭代复杂性为O（1/k）.作为应用，我们还建立了求解单调变分包含问题的惯性邻近收缩算法，求解广义变分不等式问题的惯性投影邻近点算法，及求解原始—对偶问题的惯性非精确调比部分逆算法产生点列的收敛性及相应算法的非渐近收敛率及遍历迭代复杂性.本文结果推广和改进了文献中的相应结论.最后，本文应用新的惯性交替方向乘子法用以求解LASSO问题，而且一些初步的试验结果表明了新的算法的优越性. | | 服务 | |  | 加入引用管理器 | | E-mail Alert | | RSS | | 收稿日期: 2019-06-25 | | | 基金资助:国家自然科学基金重大项目（11991024），国家自然科学基金面上项目（11171363）和重庆市基础科学与前沿技术研究专项重点项目（cstc2015jcyjBX0029）资助. |
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