论文标题
线路搜索投影算法，用于解决希尔伯特空间中没有单调性的平衡问题
A linesearch projection algorithm for solving equilibrium problems without monotonicity in Hilbert spaces
论文作者
论文摘要
我们提出了一种线条搜索投影算法，用于解决希尔伯特空间中的非占主酮和非lipschitzian平衡问题。证明，在假设相关的薄荷平衡问题的溶液集是非空的，这是由提出的算法产生的序列强烈收敛到平衡问题的解决方案。与现有方法相比，我们不使用Fejér单调性来证明融合的策略。这是由于将固定点而不是当前点投射到每个迭代处可行集的子集上。 Moreover, employing an Armijo-linesearch without subgradient has a great advantage in CPU-time.一些数值实验证明了提出算法的效率和强度。
We propose a linesearch projection algorithm for solving non-monotone and non-Lipschitzian equilibrium problems in Hilbert spaces. It is proved that the sequence generated by the proposed algorithm converges strongly to a solution of the equilibrium problem under the assumption that the solution set of the associated Minty equilibrium problem is nonempty. Compared with existing methods, we do not employ Fejér monotonicity in the strategy of proving the convergence. This comes from projecting a fixed point instead of the current point onto a subset of the feasible set at each iteration. Moreover, employing an Armijo-linesearch without subgradient has a great advantage in CPU-time. Some numerical experiments demonstrate the efficiency and strength of the presented algorithm.
