互补问题算法的新进展

The New Advances in Methods for Complementarity Problems

互补问题是一类重要的优化问题．在最近30多年的时间里，人们为求解它而提出了许多算法．该文主要介绍1990-1997年之间出现的某些新算法．它们大致可归类为：（1）光滑方程法；（2）非光滑方程法；（3）可微无约束优化法；（4）GLP投影法；（5）内点法；（6）磨光与非内点连续法．文中对每类算法及相应的收敛性结果做了描述与评论，并列出有关文献．

With the development of the research for complementarity problem (CPs forshort) which are an important class of optimization problems, a lot of methods for solving CPsare proposed. This paper is a survey of the methods which appear in 1990-1997. These methodscan be classified roughly as (1) smooth equation methods; (2) nonsmooth equation methods; (3)unconstrained optimization methods; (4) GLP projection methods; (5) interior point methods;(6) smoothing and noninterior continuation methods. Each class of them and the correspondingconvergence results are described and reviewed. Some related literature is pointed out in thispaper.