一类广义多项式互补问题的光滑化共轭梯度法  

The Smoothing Conjugate Gradient Method for a Kind of Generalized Polynomial Complementarity Problem

作　　者：郝月 杜守强 HAO Yue;DU Shouqiang(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院,青岛266071

出　　处：《应用数学学报》2022年第1期47-58,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11671220);山东省自然科学基金(ZR2016AM29)资助项目。

摘　　要：本文研究了一类广义多项式互补问题,在一定条件下,证明了其有唯一解.通过极大极小转化技术,将此类广义多项式互补问题转化为光滑化无约束优化问题进行求解,并提出了一种新的光滑化共轭梯度法.在一定假设条件下,证明了该方法的全局收敛性.最后相关的数值实验表明了算法可以有效求解广义多项式互补问题.In this paper,a kind of generalized polynomial complementarity problem is studied.Under certain conditions,we prove that the generalized polynomial complementarity problem has a unique solution.We show that the generalized polynomial complementarity problem can be converted to a smoothing unconstrained optimization problem by minimax technic,and we also propose a new smoothing conjugate gradient method for solving the proposed generalized polynomial complementarity problem.The proposed method can be proved to be globally convergent under standard assumptions.Finally,numerical results are given to illustrate that the proposed method can efficiently solve the generalized polynomial complementarity problem.

关 键 词：广义多项式互补问题 极大极小问题 共轭梯度法 全局收敛 

分 类 号：O221[理学—运筹学与控制论]