Ⅰ. INTRODUCTION In order to modify the convergence of Rosen’s algorithm, Polak used a complex ε-procedure and proved the convergence of the modified algorithm under a condition called ε-hypothesis. Zhang Xiangsun ...Ⅰ. INTRODUCTION In order to modify the convergence of Rosen’s algorithm, Polak used a complex ε-procedure and proved the convergence of the modified algorithm under a condition called ε-hypothesis. Zhang Xiangsun showed that the ε-hypothesis is equivalent to展开更多
In 1983,Du and Sun gave an algorithm which possesses superiorities of both Rosen’sgradient projection method and Wolfe’s reduced gradient method.However,in order to have theprovable global convergence,the algorithm ...In 1983,Du and Sun gave an algorithm which possesses superiorities of both Rosen’sgradient projection method and Wolfe’s reduced gradient method.However,in order to have theprovable global convergence,the algorithm includes an ε-procedure as one of its parts.In this paper,we delete such a part and prove a convergence theorem.展开更多
文摘1960年,Rosen 提出一个求线性不等式组可行解的投影算法.1981年,Powell给出一个例子说明 Rosen 的算法会发生循环从而失效.本文证明,按照 Rosen 的算法,只要适当地做点修正,循环就可避免,从而算法必在有限步内找到解或发现无解.首先给出一些记号.所考虑的问题是求 n 维向量 x
文摘Ⅰ. INTRODUCTION In order to modify the convergence of Rosen’s algorithm, Polak used a complex ε-procedure and proved the convergence of the modified algorithm under a condition called ε-hypothesis. Zhang Xiangsun showed that the ε-hypothesis is equivalent to
基金The work was supported in part by National Natural Science Foundation of China
文摘In 1983,Du and Sun gave an algorithm which possesses superiorities of both Rosen’sgradient projection method and Wolfe’s reduced gradient method.However,in order to have theprovable global convergence,the algorithm includes an ε-procedure as one of its parts.In this paper,we delete such a part and prove a convergence theorem.
