复杂流程工业系统的优化操作

ＳＱＰ方法在中小规模非线性规划中已成为主流算法，但在求解大规模优化问题时存在Ｈｅｓｓｉａｎ矩阵规模过大，存储、计算困难，以及计算量随不等式约束数量呈指数上升等缺点，简约空间ＳＱＰ法将变量分解为独立变量和非猖变量两部分。优化时只考虑独立变量，从而大大降低了变量维数，减小了Ｈｅｓｓｉａｎ矩阵规模。内点法、修改障碍函数法在求解不等式约束问题时都具有迭代次数几乎不受不等式约束规模影响的特点，因此可以将它们集成入简约空间ＳＱＰ法，使之可以更有效地对大规模优化问题求解。

Operational Optimization of Complex Process Industrial System

This paper reviews recent advances in the development of the operational optimization in process system. Successive quadratic programming (SQP) algorithm has been widely used in medium\|scale non-linear programming. But when solving large-scale models, some problems has been encountered, such as the storage requirements for the Hessian matrix, the computational expense of solving large quadratic programs, and the combinatorial complexity associated with active set QP methods. The reduced space SQP algorithm decomposes the variables into two part:the independent variables and the dependent variables, and only the independent variables are involved during optimization, which reduces the storage requirements for the Hessian matrix and the computational expense of solving QP. There are three types of the basis for the decomposition:standard orthogonal basis, orthogonal basis and coordinate basis. Mehrotra present a modified interior-point method, which can start from infeasible initial point. The modified interior-point method has been integrated into the reduced SQP algorithm, which leads more efficiency in solving large-scale optimization. The modified barrier function method integrated constraints into the object function as penalty functions. The penalty factors decrease when iterate, so that the object function can converge in the optimal point. Computational experiences show that the penalty factors affect iterations and results very much. The interior-point method and the modified barrier function method have been shown to solve large programs with many non-equal constraints much faster than the active set method.