求解变分不等式问题新的自适应投影算法

A new self-adaptive projection method for variational inequalities

目的提出求解变分不等式问题的新的自适应投影算法,并在适当条件下证明其全局收敛。方法改进已有投影算法的搜索方向并建立新的步长。结果提出了新的自适应投影算法。该算法的搜索方向和步长在解附近均不趋于零,并在映射伪单调的条件下证明了其全局收敛性。结论与已有算法相比,新算法收敛快且收敛条件弱。因此新算法的适用范围更广。

Aim To propose a new self-adaptive projection method for variational inequalities and prove that the new method is global convergence under mild condition. Methods Improve searching direction of the existing method and provide new step-size. Results The searching direction and the step-size of the proposed method are not zero near the solution, and its global convergence is proved under the pesudomotonicity of the underlying mapping. The efficience of the new method is illustrated by some preliminary computational results. Conclusion Compared with the existing methods, the new method has fast convergence and weak convergence condition, and thus it has larger application scope.