TY - JOUR AU - Kong, Zhao-Rong AU - Ceng, Lu-Chuan AU - Liou, Yeong-Cheng AU - Wen, Ching-Feng PY - 2017 TI - Hybrid steepest-descent methods for systems of variational inequalities with constraints of variational inclusions and convex minimization problems JO - Journal of Nonlinear Sciences and Applications SP - 874--901 VL - 10 IS - 3 AB - 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. 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