我們考慮有約束條件請況下凸的最小化問題
min
x C
f(x)
在本篇論文我們提供梯度投影法來產生序列 xk
, 根據下列的迭代方法
xk +1
= PC ( x (x ) k
k
k − f )
我們基本的想法是將最小化問題轉換成一個固定點的演算法:
x T k
k

=
+1 xk , k =0,1, …
來解決最小化的問題.
本篇文章我們提供了梯度投影法根據不同步長的選擇, 去討論其解的收斂
問題.

We consider the constrained convex minimization problem
min
x2C
f(x)
we will present gradient projection method which generates a sequence fxkg
according to the formula
xk+1 = PC(xk

1 Introduction 1
2 Preliminaries 2
3 The Gradient-Projection Method 6
3.1 Constant Stepsize . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Variable Stepsize . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3 Two-Slope Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 Strongly Monotone Gradient . . . . . . . . . . . . . . . . . . . . . 15
References 20

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