Iterative Schemes for Convex Minimization Problems with Constraints
Keyword(s):
We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.
2016 ◽
Vol 9
(4)
◽
pp. 421-434
2011 ◽
Vol 2011
◽
pp. 1-22
2011 ◽
Vol 12
(3)
◽
pp. 259-265