与渐进非扩张半群不动点问题有关的分裂变分包含问题及其对最优化问题的应用

Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem

该文的目的是利用收缩投影方法,引入一类迭代程序,并证明该迭代程序强收敛于Hilbert空间中分裂变分包含问题和渐进非扩张半群的不动点问题的一公解.作为应用,在文中还把所得结果应用于研究分裂最优化问题及分裂变分不等式问题.

The purpose of this paper is by using the shrinking projection method to introduce and study an iterative process to approximate a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup. As applications, we shall utilize the results to study the split optimization problem and the split variational inequality.