【摘要】 针对希尔伯特空间中的一般变分不等式,将其等价转化为变分包含问题.利用非精确邻近点算法将问题进一步转化为求解一系列子问题,给出了一种近似解子问题的新误差准则,结果表明:在该准则下,非精确邻近点算法具有全局收敛性.在算子F是g-单调和算子g是同胚映射的条件下,得到非精确邻近点算法收敛于一般变分不等式的一个解,证明了解是唯一的.更多还原

【Abstract】 Aiming at the variational inequality in Hilbert space, this paper transformed it into variational inclusion problem equivalently. It was further transformed into solving a series of subproblems by using inexact proximal point method and provided a new error criterion to solve the subproblems approximately. The results show that this algorithm is convergent globally under the new criterion. Under the conditions that the operator F is g-monotone and the operator g is homeomorphism, this study concluded that the inexact proximal point algorithm converges to a solution of general variational inequality and proved that the solution is unique.更多还原