逼近精确罚函数法求解单阶段随机规划

An Approximation-exact Penalty Function Method of Solving Single Stage Stochastic Programming

提出了一种求解单阶段随机规划的算法——逼近精确罚函数法.首先,通过离散化随机变量的方法得到逼近原问题的确定非线性规划序列,然后,建立精确罚函数并构造无约束最优化问题.在一定的条件下,证明了确定非线性规划序列与无约束最优化问题的等价性,同时也证明了离散序化的解序列收敛到原规划的解.

An approximation-exact penalty function method for solving single stage stochastic programming is presented.Firstly,the determinate nonlinear programming sequences are obtained by means of discretizing random variable.Secondly,an exact penalty function and an unconstrained optimization are constructed correspondingly.Under lenient conditions,some equivalent properties between the determinate nonlinear programming and the unconstrained optimization are proved,and the solution sequence of the determinate nonlinear programming converges to solution to the original problem in some sense.