研究了数学规划的一种障碍目标罚函数算法,首先,针对数学规划问题定义了一种障碍目标罚函数,针对凸规划问题,提出了一种求解近似最优解的算法,并证明了对应的收敛性,然后,针对一般数学规划问题又提出一个改进算法,并证明了对应的收敛性,最后,数值实验结果表明了提出的改进算法比传统的障碍函数算法有更好的收敛性.

In this paper, we study an algorithm of a barrier objective penalty function for mathematical programming. We define the barrier objective penalty function for mathematical programming. Based on the barrier objective penalty function, we present an algorithm (called B Algorithm) for finding an approximately optimal solution to a convex mathematical programming and prove its convergence under some conditions. Then, we obtain an algorithm (called MB Algorithm) by modifying B Algorithm and its convergence without convex conditions. Finally, numerical examples show that MB Algorithm has much better convergence than classical barrier function algorithms.