Chen Haibin, Wang Yiju, Xu Yi
1School of Management Science, Qufu Normal University, Rizhao Shandong, China.
2Department of Applied Mathematics, Southeast University, Nanjing, China.
J Inequal Appl. 2018;2018(1):26. doi: 10.1186/s13660-018-1619-9. Epub 2018 Jan 30.
For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion property with respect to a given initial point. The global convergence of the method is established under the assumptions of pseudomonotonicity of the equilibrium function and of continuity of the underlying multi-valued mapping. Furthermore, we show that the generated sequence converges to the nearest point in the solution set to the initial point. Numerical experiments show the efficiency of the method.
对于参与者的成本及其策略都依赖于对手决策的拟均衡问题，设计了一种用于求解该问题的交替外梯度投影方法。与经典外梯度投影方法不同，经典方法生成的序列相对于解集具有收缩性质，而新设计的方法相对于给定的初始点具有扩张性质。该方法的全局收敛性是在均衡函数的伪单调性和基础多值映射的连续性假设下建立的。此外，我们表明生成的序列收敛到解集中距离初始点最近的点。数值实验表明了该方法的有效性。
