大规模过程系统优化的序列界约束方法

来源期刊：中南大学学报(自然科学版)2004年第3期

论文作者：梁昔明 李文革

文章页码：434 - 437

关键词：过程系统优化;大规模非线性规划;序列界约束方法;数值试验

Key words：process system optimization; large-scale nonlinear constrained minimization; successive bound constrained programming algorithms; numerical experiment

摘    要：基于非线性约束极小化的序列无约束方法,对大规模过程系统稳态优化的序列界约束方法进行了研究。该约束方法的罚函数只包含对等式和/或不等式约束的惩罚项,不包含对界约束的惩罚项,通过迭代求解一系列界约束极小化子问题而非无约束极小化子问题获得原问题的解;算法按2层结构实现,内层结构中主要求解界约束极小化子问题得到下一个迭代点,外层迭代主要修改乘子向量和罚向量以及检查收敛准则是否满足,重构下次迭代的界约束子问题,或在收敛准则满足时终止算法。此外,给出了求解界约束极小化子问题的修改截断Newton法,并用一类规模可变的约束优化问题和一类最优控制问题对所给方法进行了数值试验,试验结果表明,所给序列界约束方法是非常稳定和有效的。

Abstract: Based on successive unconstrained programming methods, the successive bound constrained programming algorithms for large-scale process system optimization are studied in this paper. A series of bound constrained sub-problems instead of a series of unconstrained sub-problems are solved is these algorithms. Since Lagrange function only contains the penalty terms for equality and inequality constraints, a modified truncated Newton algorithm is proposed to solve the bound constrained sub-problems. The successive bound constrained programming algorithms are performed in two stages. The inner stage is the bound constrained minimization of the augmented Lagrange penalty function in which a new set of primal variables is found. The outer stage is performed to update the Lagrange multipliers and penalty parameters, check for convergence and accordingly reinitiate another bound constrained minimization or declare convergence. Numerical experiments are made for two kinds of alterable dimension nonlinear programming problems, which proves the stability and effectiveness of the algorithms for chemical process optimization.