本文研究二次極小化問題之梯度投影法的強收斂性問題。特點是約束集合之結構放鬆為有限多個非擴張映射固定點之交集，而我們所提出的迭代方法完整的用非擴張映射替代了投影算子，從而避免投影的計算問題，進而改進了二次規劃之梯度投影法。

In this paper we study the strong convergence of a gradient-projection method for quadratic minimization problem. The trait is that the structure of constraints set relax to the intersection of xed point of nite nonexpansive mapping, and we proposed the iterative method that nonexpansive mapping to replace projection operator completely, to avoid the problem of the calculation of projected operator, and improved gradient-projection method of quadratic minimization problem further.

審定書 i
摘 要 ii
Abstract iii
Table of Contents iv
1 Introduction........1
2 Preliminaries......2
3 Main Results......6
References...........13

References
[1] O'Hara J. G., Pillay P., and Xu H. K., Iterative Approaches to Convex Minimization Problems, Numerical Functional Analysis and Optimization. 25 (5&6)(2004), 531-546.
[2] Reich S., and Xu H. K., An Iterative Approach to a Constrained Least Squares Problem, Abstract and Applied Analysis. 8 (2003), 503-512.
[3] Xu H. K., An iterative approach to quadratic optimization, J. Optimiz. Theory Appl. 116 (2003), 659-678.
[4] Goebel K., and Kirk W. A., Topics in Metric Fixed Point Theory, Cambridge University Press (1990).
[5] Kreyzig, E., Introductory Functional Analysis with Applications, John Wiley and Sons (1978).