Ishikawa型黏性逼近迭代及其在双层优化问题中的应用  

The Ishikawa Viscosity Approximation Iteration and Its Application to Bi-level Optimization Problems

作　　者：青飞宇 王涛 QING Feiyu;WANT Tao(College of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院

出　　处：《内江师范学院学报》2019年第10期35-41,共7页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11871059、11371015);四川省高校创新团队(16TD0019);西华师范大学英才基金(17YC379)

摘　　要：Ishikawa迭代和黏性逼近迭代在非扩张映射的不动点问题的研究中扮演着重要角色.提出Ishikawa型黏性逼近迭代方法,简称IVM,该方法可以退化为经典的黏性逼近迭代方法.在适当条件下,证明了IVM的强收敛性.将所得的收敛性结果应用于求解双层优化问题,得到一个求解双层优化问题的算法,并且证明该算法强收敛到双层优化问题的解.Ishikawa iteration and viscosity approximation iteration play an important role in the study of fixed point problems of non-expansive mappings. An Ishikawa viscosity approximation iterative method,(IVM for short) is proposed. The said method can be reduced to classical viscosity approximation iterative method. Under appropriate conditions, the strong convergence of IVM is proven. As an application, the convergence results were applied to solve the bi-level optimization problems, and an algorithm to solve the bi-level optimization problems was obtained, and it is proven that the algorithm strongly converges to the solution of the bi-level optimization problems.

关 键 词：ISHIKAWA迭代 黏性逼近迭代 非扩张映射 强收敛 双层优化 

分 类 号：O221[理学—运筹学与控制论]