全局收敛的投影单纯形方法

对于线性约束、非线性目标的优化问题，文献［１］的作者以极小化条件代替求正交投影的一组正交条件，并用一个特殊的线性规划模型来确定迭代方向，由此给出了一个算法。但文献［１］没有讨论算法的收敛性，且一般说来，这种算法不具备收敛性质［５］。本文沿用［１］的迭代方向ｄ（ｘ）的表示形式，给出了一个新的算法，讨论了算法性质，证明了算法具有全局收敛性.

A Projective Simplex Algorithm with Global Convergence Property

In Ref.,an algorithm had been given for the optimized problem with linear constraints and nonlinear objective function.In this algorithm, a special linear programming model in which a group of normal projective condltions substituted by minimized conditions had been considered to determine the iterative direction.But the convergence of the algorithm had no discussed and this type of the algorithm had generally no the convergence property.In this paper, a new algorithm with the same formula of iterative direction d(x) that given in had been proposed, some properties of the algorithm had been discussed and the proof global convergence of the algorithm had been given.