关于吴方法在双层规划中的一个应用

双层规划及多层规划这一数学规划研究中的较新领域因其坚实的经济背景及丰富的数学内涵在二十年来的发展过程中变得越来越吸引人们的关注. 在通常解双层规划问题时往往采用数值计算的方法, 得到的解并不一定是全局最优解. 该文介绍了一个全新的解双层规划问题的方法,它与数值计算法不同, 采用的是符号计算, 依据了计算机代数与代数几何的理论. 作者通过对文献1]中的几个双层规划问题的上机计算, 得出了与之不同的全面彻底的解答, 在比较过程中, 发现不仅所得的结果要比文献1]中答案更进一步, 而且也证明了文章的新方法在解这一类问题时,是简明和行之有效的.

On Applications of Wu's Method in Bilevel-Programming Problems

The bilevel-programming problems are important in mathematical applications. They are usually solved by various kinds of numerical methods. This will give solutions in the form of local extremal values but not necessarily global optimal ones. Consider the case for which all functions occurred in the bilevel-programming problems are polynomial ones. The present paper shows how to solve the problems by the MM-method (Mathematics-Mechanization method) or Wu's method. Wu's method is different from the numerical methods in that the computations are symbolic instead of numerical ones. Theoretically it is based on computer algebra and algebraic geometry. The author uses the computer to get complete blobal solutions of some practical test problems in the bilevel-programming. The computations show that Wu's method furnishes the true optimal values of the bilevel-programming problems, and is also quite efficient.