线性约束凸规划的鞍梯度法

求线性约束凸规划问题的最优解。方法：在鞍梯度法的基础上提出了一个具有全局收敛性的原一对偶外点算法。结果：每步迭代利用Lagrange函数的鞍梯度构造搜索方向，生成次可行解序列，由此得到的序列的极限就是原-对偶问题的最优解。结论：即使从原一对偶问题的不可行点开始迭代算法也收敛。

The Saddle-Gradient Method for Linear Constrained Convex Programming

Objective: To search optimal solutions of convex programming problems with linear constraints. Method: A globally convergent primal-dual exterior-point algorithm is proposed based on the saddle-gradient method. Result: The saddle-gradient of Lagrange function is utilized to construct the search directions and generate the sub-feasible solutions sequence , then we prove that the limit of the sequence is the optimal solution of the primal-dual problem. Conclusion: The algorithm is convergent even if it iterates from an infeasible point of the primal-dual problem.