带参数扰动的原始对偶内点算法求解一类非线性规划问题

摘要

This paper presents a new primal-dual interior point method for solving general nonlinear programming problems.The improved primal-dual interior point method may change the shapes of feasible region in order to expand the region of initial points,and get the descent direction of the merit function by the modified Newton method.The convergence of primal-dual interior point method with parameter perturbation was presented and the effectiveness of the algorithm was shown by two examples.%给出一种通过新的原始对偶内点法求解一类非线性规划问题的算法及带参数扰动的原始对偶内点法的收敛性，并通过数值实例说明了该算法的有效性。该算法改进了原始对偶内点法，可由参数控制可行域的形状，扩大了初始点的选择范围，并通过修正牛顿法找到值函数的下降方向。