具有约束条件的均衡规划问题的微分方程方法  

A differential equation method for solving equilibrium programming with constraints

作　　者：王莉[1] 王虎彬[1] 王诗云[1] 孙菊贺[1] 

机构地区：[1]沈阳航空航天大学理学院,沈阳110136

出　　处：《沈阳师范大学学报（自然科学版）》2013年第4期466-470,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金数学天元基金资助项目(11126066);沈阳航空航天大学2013年博士启动基金资助项目(13YB14;13YB15)

摘　　要：提出了具有不等式约束的均衡规划问题,运用该均衡规划问题的拉格朗日函数和投影算子将具有不等式约束的均衡规划问题转化为方程组。进一步,应用所得到的方程组建立了具有控制过程的微分方程系统,并证明了具有控制过程的微分方程系统的解的聚点是具有不等式约束的均衡规划问题的解。最后,给出了2个具有不等式约束的均衡规划问题的数值算例,并分别运用具有控制过程的微分方程系统对其进行求解,描绘了每个算例的微分方程系统的解的轨迹图,从图中可以明显地观察到具有控制过程的微分方程系统的解的轨迹收敛于均衡规划问题的解,从而说明了微分方程方法求解具有不等式约束的均衡规划问题的可行性和有效性。The equilibrium programming with inequality constraints is proposed, and the equilibrium programming with inequality constraints is transformed into an equation system based on Lagrange function and projection operator of the equilibrium programming with inequality constraints. Furthermore, a differential equation system with controlled process is established by using the equation system. It is proved that the accumulation points of the trajectories of this kind of differential equation system are the solutions to the equilibrium programming with inequality constraints. At last, two numerical examples of the equilibrium programming with inequality constraints are provided, and these two examples are solved by using the system of differential equation with controlled process. The transient behaviors of the trajectories of the differential equation system with controlled process for every example are illustrated. It can be seen clear that the trajectories of the differential equation system with controlled process converge to the solutions of the equilibrium programming with inequality constraints, that show the feasibility and effectiveness of the differential equation method for solving equilibrium programming with constraints.

关 键 词：均衡规划 微分方程 拉格朗日函数 投影算子 

分 类 号：O221.2[理学—运筹学与控制论] O175.14[理学—数学]