Abstract
It is well known that the regularization method plays an important role in solving a constrained convex minimization problem. In this article, we introduce implicit and explicit iterative schemes based on the regularization for solving a constrained convex minimization problem. We establish results on the strong convergence of the sequences generated by the proposed schemes to a solution of the minimization problem. Such a point is also a solution of a variational inequality. We also apply the algorithm to solve a split feasibility problem. MSC:47H09, 47H05, 47H06, 47J25, 47J05.
Highlights
The gradient-projection algorithm is a classical power method for solving constrained convex optimization problems and has been studied by many authors
Consider the problem of minimizing f over the constraint set C
The purpose of this paper is to present the general iterative method combining the regularization method and the averaged mapping approach
Summary
The gradient-projection algorithm is a classical power method for solving constrained convex optimization problems and has been studied by many authors (see [ – ] and the references therein). Consider the problem of minimizing f over the constraint set C (assuming that C is a nonempty closed and convex subset of a real Hilbert space H). We first propose implicit and explicit iterative schemes for solving a constrained convex minimization problem and prove that the methods converge strongly to a solution of the minimization problem, which is a solution of the variational inequality.
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