A relaxed self-adaptive CQ algorithm for the multiple-sets split feasibility problem

作者：He Songnian^*; Zhao Ziyi; Luo Biao

来源：Optimization, 2015, 64(9): 1907-1918.

DOI：10.1080/02331934.2014.895898

• multiple-sets split feasibility problem
• relaxed CQ algorithm
• Hilbert space
• strong convergence
• bounded linear operator

The multiple-sets split feasibility problem (MSFP) is to find a point belongs to the intersection of a family of closed convex sets in one space, such that its image under a linear transformation belongs to the intersection of another family of closed convex sets in the image space. Many iterative methods can be employed to solve the MSFP. Jinling Zhao et al. proposed a modification for the CQ algorithm and a relaxation scheme for this modification to solve the MSFP. The strong convergence of these algorithms are guaranteed in finite-dimensional Hilbert spaces. Recently Lopez et al. proposed a relaxed CQ algorithm for solving split feasibility problem, this algorithm can be implemented easily since it computes projections onto half-spaces and has no need to know a priori the norm of the bounded linear operator. However, this algorithm has only weak convergence in the setting of infinite-dimensional Hilbert spaces. In this paper, we introduce a new relaxed self-adaptive CQ algorithm for solving the MSFP where closed convex sets are level sets of some convex functions such that the strong convergence is guaranteed in the framework of infinite-dimensional Hilbert spaces. Our result extends and improves the corresponding results.

• 出版日期2015-9-2
• 单位中国民航大学