On the convergence of the projected gradient method
On the convergence of the projected gradient method
复制标题
关于投影梯度法的收敛性
DOI：
10.1007/bf00940786
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发表时间：
1993
影响因子：
1.9
通讯作者：
G. Fournier
中科院分区：
文献类型：
--
作者：
J. Dussault;G. Fournier
研究了线性约束优化的投影梯度算法。Wolfe （Ref. 1）提出了一个反例来证明该算法可以阻塞。然而，他的反例仅为∑1(∑n)，并推测该算法对于∑2函数是收敛的。我们证明这个猜想是部分正确的。我们还表明，由于我们提出了一系列反例，因此需要更多的假设来证明收敛性。最后给出了二次目标函数不会产生干扰的证明。
We study the projected gradient algorithm for linearly constrained optimization. Wolfe (Ref. 1) has produced a counterexample to show that this algorithm can jam. However, his counterexample is only ℒ1(ℝn), and it is conjectured that the algorithm is convergent for ℒ2-functions. We show that this conjecture is partly right. We also show that one needs more assumptions to prove convergence, since we present a family of counterexamples. We finally give a demonstration that no jamming can occur for quadratic objective functions.