向量均衡问题的一个投影迭代解法  

An iterative algorithm for vector equilibrium problems

作　　者：成波[1,2] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院,西安710071 [2]安康学院数学系,陕西安康725000

出　　处：《兰州大学学报（自然科学版）》2009年第5期105-109,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(60574075)

摘　　要：将用于求解欧氏空间上数量均衡问题的一种投影迭代法进行了推广,并将这种推广的投影迭代法用于求解欧氏空间上的向量均衡问题。利用非线性标量化函数,将向量优化问题化为相应的数量优化问题,研究了投影迭代法对向量均衡问题的收敛性。结果表明推广的投影迭代法对满足一定条件的向量均衡问题是收敛的。A projection iterative algorithm for solving scalar equilibrium problems was generalized to solve a vector equilibrium problem defined on Euclidean space. By using nonlinear scalarization function, the vector optimization problems were changed into the scalar optimization problems. In this way, a convergence analysis of the algorithm for solving the vector equilibrium problem was given, with the result that the algorithm was converged under some appropriate conditions.

关 键 词：向量均衡问题 投影迭代法 非线性标量化函数 凸可行性问题 

分 类 号：O224[理学—运筹学与控制论]