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中南大学学报(自然科学版)

Journal of Central South University

第35卷    第3期    总第157期    2004年6月

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文章编号:1672-7207(2004)03-0434-04
大规模过程系统优化的序列界约束方法
梁昔明,李文革

(中南大学信息科学与工程学院,湖南长沙,410083)

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。

 

关键字: 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

Successive bound constrained minimization for
large-scale process system optimization
LIANG Xi-ming, LI Wen-ge

College of Information Science and Engineering, Central South University, Changsha 410083, China

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.

 

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

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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