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摘要
The constrained convex minimization problem is to find a point x* with the property that x* epsilon C, and h(x*) = min h (x), for all x epsilon C, where C is a nonempty, closed, and convex subset of a real Hilbert space H, h (x) is a real-valued convex function, and h(x) is not Frechet differentiable, but lower semicontinuous. In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms. We firstly construct a bifunction F-1(x,y) defined as F-1(x,y) = h(y) - h(x). And we ensure the equilibrium problem for F-1(x,y) equivalent to the above optimization problem. Then we use iterative methods for equilibrium problems to study the above optimization problem. Based on Jung's method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem. In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem. The results of this paper extend and improve some existing results.
- 出版日期2014
- 单位中国民航大学
