Hybrid steepest-descent methods for systems of variational inequalities with constraints of variational inclusions and convex minimization problems

Kong, Zhao-Rong¹ ; Ceng, Lu-Chuan² ; Liou, Yeong-Cheng³ ; Wen, Ching-Feng⁴

¹ Economics Management Department, Shanghai University of Political Science and Law, Shanghai 201701, China
² Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
³ Department of Healthcare Administration and Medical Informatics, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan
⁴ Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan;Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 3, p. 874-901.

Résumé

Two hybrid steepest-descent schemes (implicit and explicit) for finding a solution of the general system of variational inequalities (in short, GSVI) with the constraints of finitely many variational inclusions for maximal monotone and inversestrongly monotone mappings and a minimization problem for a convex and continuously Fréchet differentiable functional (in short, CMP) have been presented in a real Hilbert space. We establish the strong convergence of these two hybrid steepestdescent schemes to the same solution of the GSVI, which is also a common solution of these finitely many variational inclusions and the CMP. Our results extend, improve, complement and develop the corresponding ones given by some authors recently in this area.

Détail

DOI : 10.22436/jnsa.010.03.03

Classification : 49J30, 47H09, 47J20, 49M05
Keywords: Hybrid steepest-descent method, system of variational inequalities, variational inclusion, monotone mapping.

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