這篇論文中，我們探討強凸函數在某非擴張映射之固定點集合上的極小化問題，我們使用正則化的技巧，並引用隱式和顯式兩種迭代方法求解唯一極小點，我們證明了兩種方法的強收斂性，我們的方法推廣了求解約束最佳化問題的梯度投影法。

In this paper we deal with the problem of minimizing a strongly convex objective function over the set of fixed points of a nonexpansive mapping T. This extends the constrained strongly convex minimization problem over a closed convex subset C of a Hilbert space since the projection Pc is nonexpansive. By introducing a parameter λ>0 , we define a family of contractions Tλ, each of which has a unique fixed point denoted as ξλ. We first prove that as λ→0, ξλ converges in norm to the unique solution of our minimization problem. We then introduce an iteration algorithm by discretization of the mappings Tλ, and prove strong convergence of this algorithm under appropriate conditions imposed on the sequence of parameters of the algorithm.

1. Introduction ------- 1
2. Preliminaries ----- 4
3. Main Results ----- 6
References ------- 13

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