非线性不等式约束最优化问题一个新的广义既约梯度法

A NEW GENERALIZED REDUCED GRADIENT METHOD FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION PROBLEMS

本文借助一种新的求基转轴运算建立了带非线性不等式约束最优化问题的一个新的广义既约梯度法．算法不引入任何松驰变量，以致扩大问题的规模，也不需对约束函数和变量的界预先估计．另一重要特点是方法不再使用隐函数理论确定搜索方向，而是由简单的显式给出．因此方法计算量小，结构简单，便于应用．对于非Ｋ—Ｔ点ｘ，我们构造的方向为可行下降的．本文证明了算法具有全局收敛性．

In this paper, a new generalized reduced gradient method for optimization problems with nonlinear inequality oonstraints is presented with the help of a new pivoting operation. This algorithm does not introduce any slack vector which may increase the scale of the problem,and meedn't estimate the bounds of constrained functions and vectors in advance. Another important feature is that it does not use implicit fuoction theory to determine the search direction any more, but it is given by a simple determined formula. Theorefore the method bas small amount of computing,simple construction, and is convenient fot use. If x is not a K-T point, the direction given is feasible descent. The global convergence of the new method is proved in this paper.