Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces

Abstract

In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.Keywords: Split monotone variational inclusion problem, maximal monotone operator, inverse strongly monotone operator, convergence theorems.

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

“…where {r n } ⊂ (0, +∞) and J A r n = (I + r n A) −1 is the resolvent of the maximal monotone operator A corresponding to the control sequence {r n }. Several iterative algorithms have been proposed by authors in the literature for solving Problem (3) and related optimization problems, see [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…where A i is a finite family of maximal monotone operators. There have been some iterative algorithms for approximating the solution of (10) in the literature, (see [37] and the references therein).…”