假設F在實Hilbert空間H中為一非線性算子，且在H之非空閉凸子集C中為強單調與Lipschitzian。也假設C是在H中非擴張映射所成之有限多個固定點集合的交集。
本文裡我們將Xu和Kim的論文(Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003 )中之迭代式做了細微改變後，利用此迭代式對任意在H中之初始點x0造出一個{xn}序列。而證明此序列{xn}在與Xu和Kim加於參數上之條件的不同下強收斂到變分不等式之唯一解u*。其中也包含了對具約束條件之廣義偽反映射的應用。

Assume that F is a nonlinear operator on a real Hilbert space H which is strongly monotone and Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We make a slight modification of the iterative algorithm in Xu and Kim (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003), which generates a sequence {xn} from an arbitrary initial point x0 in H. The sequence {xn} is shown to converge in norm to the unique solution u* of the variational inequality, under the conditions different from Xu and Kim’s ones imposed on the parameters. Applications to constrained generalized pseudoinverse are included. The results presented in this paper are complementary ones to Xu and Kim’s theorems (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003).

1 Introduction 4
2 Preliminaries 10
3 Hybrid Steepest-Descent Algorithms with Variable Parameters 12
4 Applications to Constrained Generalized Pseudoinverse 23
References 27

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