Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem

Volume 9, Issue 9, pp 5316--5331 http://dx.doi.org/10.22436/jnsa.009.09.01

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Authors

Ming Tian - College of Since, Civil Aviation University of China, Tianjin 300300, China. - Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China. Hui-Fang Zhang - College of Since, Civil Aviation University of China, Tianjin 300300, China.

Abstract

The gradient-projection algorithm (GPA) is an effective method for solving the constrained convex minimization problem. Ordinarily, under some conditions, the minimization problem has more than one solution, so the regulation is used to find the minimum-norm solution of the minimization problem. In this article, we come up with a regularized gradient-projection algorithm to find a common element of the solution set of equilibrium and the solution set of the constrained convex minimization problem, which is the minimum-norm solution of equilibrium and the constrained convex minimization problem. Under some suitable conditions, we can obtain some strong convergence theorems. As an application, we apply our algorithm to solve the split feasibility problem and the constrained convex minimization problem in Hilbert spaces.

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Keywords

• Iterative method
• equilibrium problem
• constrained convex minimization problem
• variational inequality
• regularization
• minimum-norm.

MSC

•  47H10
•  54H25

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