一类随机非线性规划的积极集SQP算法

An active set SQP algorithm for a class of stochastic nonlinear programming

在等价非线性扩展模型的基础上,给出了求解一类随机非线性规划的序列二次规划(sequential quadratic programming,简称SQP)算法.与标准SQP算法不同,本文算法采用积极集方法求解SQP子问题以加快收敛速度,并采用滤子方法确定搜索步长,克服了传统方法选取惩罚因子的困难.在一定条件下证明了所给算法的收敛性.最后,通过一个数值例子验证了该方法的有效性.

We present a sequential quadratic programming（SQP） method for solving a class of stochastic nonlinear programming based on the certainty extended nonlinear model. The method has two points that are different from the standard SQP method. First, the SQP subproblems are solved by combining with the active set method so as to speed up the convergence. Second, the step length is obtained by the filter method, which overcomes the difficulty of choosing penalty factor in the standard method. A convergent theorem is proved under certain conditions,and a numerical example is given to demonstrate the efficiency of the algorithm.