一种多维连续型动态规划的新算法  

New algorithm for multidimensional continuing dynamic programming

作　　者：张鹏[1] 

机构地区：[1]武汉科技大学管理学院,武汉430081

出　　处：《控制与决策》2011年第8期1219-1223,共5页Control and Decision

基　　金：教育部人文社会科学基金项目(08JC630062);湖北省社会科学基金项目"十一五"规划课题([2010]102);湖北省自然科学基金项目(2010CDB03304)

摘　　要：在求解一维连续型动态规划问题的自创算法——离散近似迭代法的基础上,结合双收敛方法,对多维连续型动态规划问题进行计算.该算法的基本思路为:在给定其他状态向量序列的基础上,每次对一个状态变量序列进行离散近似迭代,并找出该状态变量的最优序列,直到所有状态向量序列都检查完.当模型为非凸非凹动态规划时,证明了该算法的收敛性;当模型为凸动态规划时,证明了该算法的线性收敛性.最后,通过具体算例验证了该模型和算法的有效性.The paper uses the discrete approximate iteration method and bi-convergent method to solve the multidimensional continuing convex dynamic programming model. Firstly, the state value of one of state equations is set to be unknown and the others be known. Then, discrete approximate iteration method is used to find the optimal value of the unknown state values until all state equations have found optimal values. If the objective function is non-concave and non-convex, the algorithm is proved convergent. If the objective function is convex, the algorithm is proved linear convergent. Finally, an example shows the effectiveness of the formation and the algorithm.

关 键 词：动态规划问题 多维 离散近似迭代方法 双收敛法 

分 类 号：O221.2[理学—运筹学与控制论]