寻找非线性规划问题Kuhn-Tucker点的一种微分方程方法(英文)

A differential equation approach to finding a Kuhn-Tucker point of a nonlinear programming problem

为了寻找带有等式约束和不等式约束的非线性规划问题的Kuhn-Tucker点,给出了一种微分方程系统.在一定的条件下,证明了非线性规划问题的Kuhn-Tucker点是微分方程系统的渐进稳定平衡点,并且基于一般微分方程系统的数值积分建立了一个数值算法,然后给出了该数值算法的收敛性定理.数值算例表明了该算法的有效性.

A system of differential equations is constructed to find Kuhn-Tucker points of a nonlinear programming problem with both equality and inequality constraints. It is proved that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the differential system and a numerical algorithm is given based on the numerical integration of the proposed system of ordinary differential equations. The convergence theorem of the numerical algorithm is demonstrated. Several illustrative examples show the effectiveness of the algorithm.