Banach空间中广义混合变分不等式解的迭代算法

Iterative Algorithm for Solving Generalized MixedVariational Inequalities in Banach Spaces

利用R.S.Burachik和S.Scheimberg(SIAM J Control Optim,2001,39(5):1633-1649.)介绍的近似点算法和Bregman泛函,在自反Banach空间中建立了一类广义混合变分不等式解的迭代算法,证明了迭代序列是有定义的,并且弱收敛于广义混合变分不等式的解.同时,给出了广义混合变分不等式解的存在性的一个充分必要条件.

By using the proximal point method introduced by Burachik and Scheimberg（SIAM J Control Optim,2001,39（5）：1633-1649.） and the Bregman function,we construct an iterative algorithm for finding the approximate solutions of a class of generalized mixed variational inequalities in reflexive Banach spaces.We prove that the sequence of approximate solutions is well-defined and converges weakly to the exact solution of the generalized mixed variational inequality.We also give a sufficient and necessary condition for the existence of solution of the generalized mixed variational inequality.