| In this paper, we consider a convex optimization problem over the fixed point set of a nonexpansive mapping, and present an ergodic iteration method for this problem together with its convergence analysis. The proposed algorithm has two features: one is that it can be applied to more general case, where the objective function is convex and Fréchet differentiable and has the hemicontinuous gradient; and the other is that as compared with the existing methods for convex optimization problems with Fréchet differentiable objective functions, the proposed algorithm does not require to solve any auxiliary optimization problems. To demonstrate convergence of the proposed method, we present numerical examples for some quadratic optimization problems over the fixed point set. |
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