一类非单调互补问题的Canonical对偶问题研究

对于一类具有广泛应用背景的非单调互补问题,我们构建了这类问题的Canonical对偶问题。其对偶问题可以写成和原问题类似的互补问题。我们给出了对偶问题和原问题解之间的对偶关系,并且将对偶问题转化成一个一维优化问题,这不但可以方便的求解这类问题,也为研究这类问题性质提供了一个非常直观的研究工具。最后,本文给出了几个算例来演示对偶问题的性质。

Canonical Duality for a Class of Nonmonotone Complementarity Problems

We construct a canonical dual problem for a class of non-monotonic complementary problems with a wide range of applications.The dual problems can be written as complementary problems with the same structure to the original problem.We discuss the relationship between the solution of the dual problem and that of the original problem.Then we transform the dual problem into a one-dimensional optimization one,which not only can be easily solved,but also provides a very intuitive research tool for studying the properties of this kind of problem.Finally,we give a few examples to demonstrate the properties of the dual problem.