解约束最优化问题的凝聚函数法

摘要

凝聚函数法（AFM）是用于求解约束最优化问题的有效方法之一，然而，凝聚函数法本身存在解发散和数据溢出问题。为系统地解决凝聚函数法的以上缺陷，本文提出一种全新的凝聚函数，通过增加稳定项来解决解发散的问题，增加指数渐消因子解决数值计算中的数据溢出问题。此外，本文还给出凝聚函数和改进的凝聚函数的性质。%In this paper,the aggregate function method(AFM)for constrained optimization prob-lems(COP)is investigated. The AFM is effective for solving multiple inequality-constrained optimiza-tion problems. However,the inherent demerits of the AFM,both in convergence and data overflow, seem to have gone unnoticed. To address these issues systematically,some necessary measures have beem taken to deal with such problems,such as adding the stable term and introducing the exponent reduction parameter to the original aggregate function,which are highlighted in the entire paper. More-over,the associated properties of both the AFM and the improved AFM(IAFM)are presented.