非凸变分不等式和非扩张映象的Wiener-Hopf方法

Wiener-Hopf equation technique for nonconvex variational inequalities and nonexpansive mappings

介绍了一类新的包含非扩张映象的非线性Wiener-Hopf方程,建立了非凸变分不等式问题与Wie-ner-Hopf方程的等价关系,进一步给出了一个求解非凸变分不等式和非扩张映象不动点的逼近方法,并在算子具有α-强制性的条件下证明了该方法所产生的迭代序列的强收敛性.

A new class of nonlinear Wiener - Hopf equations with a nonexpansive mappings is introduced. The equivalence between the Wiener - Hopf equations and nonconvex variational inequality is established to ana- lyze an iterative scheme for finding a common element of the set of solutions of the nonconvex variational inequal- ity and the set of fixed points of nonexpansive mappings. The convergence analysis of the approximation methods is also cosidered under ,qamt~ ~nitahl~ t,,~ndit;,~n~