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

Suwannaprapa, Montira ¹ ; Petrot, Narin ²

¹ Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
² Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand;Centre of Excellence in Nonlinear Analysis and Optimizations, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 683-700.

Résumé

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.

Détail

DOI : 10.22436/jnsa.011.05.09

Classification : 49J53, 26A18
Keywords: Split monotone variational inclusion problem, maximal monotone operator, inverse strongly monotone operator, convergence theorems

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