基于控制思想求解非线性规划问题的李雅普诺夫方法

Lyapunov Method for Solving Nonlinear Programming Problems Based on Control Ideas

为了高效求解非线性规划问题,对一种基于控制思想的新颖方法——李雅普诺夫方法——进行了研究.该方法将约束非线性规划问题转化为一个动态系统,基于系统的动态特性给出原优化问题的最优解.分别针对单目标和多目标的非线性规划问题,对算法的收敛性进行了分析,给出了算法在应用时松弛变量、增益因子等关键参数的取值建议.大量数值算例验证了上述收敛性及参数取值建议的正确性,表明了该方法在求解非线性规划问题时的巨大潜力和新颖性.

In order to solve nonlinear programming problems efficiently,a novel optimization method named Lyapunov theory-based method(for short,Lyapunov method)based on control ideas is studied.This method transforms a constrained nonlinear programming problem into a dynamic system and presents optimal solution of the original optimization problem according to the dynamic characteristics of the system.Regarding to the single-objective and multi-objective nonlinear programming problems,the convergence of the algorithm is analyzed,and potential values of the key parameters such as the slack variables and gain factors in applications of the algorithm are suggested.A large number of numerical instances verify the aforementioned convergence and the correctness of the proposed parameter values,indicating the great potential and novelty of the method in solving nonlinear programming problems.