Iterative algorithms for finding the zeroes of sums of operators

作者：Shi, Luo Yi; Chen, Rudong^*; Wu, Yujing

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 2014(1): 349.

DOI：10.1186/1029-242X-2014-349

• split equality problem
• iterative algorithms
• converge strongly

Let H-1, H-2 be real Hilbert spaces, C subset of H-1 be a nonempty closed convex set, and 0 is not an element of C. Let A : H-1 -> H-2, B : H-1 -> H-2 be two bounded linear operators. We consider the problem to find x is an element of C such that Ax = -Bx (0 = Ax + Bx). Recently, Eckstein and Svaiter presented some splitting methods for finding a zero of the sum of monotone operator A and B. However, the algorithms are largely dependent on the maximal monotonicity of A and B. In this paper, we describe some algorithms for finding a zero of the sum of A and B which ignore the conditions of the maximal monotonicity of A and B.

• 出版日期2014-9-8
• 单位天津工业大学; 天津市职业大学