线性二层规划扩展KT方法研究

Discussion on the Extended KT Approach for Linear Bilevel Programming

为了更好地解决上层带有任意线性约束的线性二层规划问题,Shi Chenggen提出了能够求解更广泛线性二层规划问题的扩展KT方法。具体介绍了求解线性二层规划的原KT方法以及扩展KT方法,同时给出了一个用扩展KT方法和用原KT方法可以得到不同最优解的算例。算例结果表明,对有些线性二层规划问题,扩展KT方法能够得到与原KT方法不同的最优解。提出了2种KT方法的等价性条件。算例结果证实了上述等价性条件的正确性。

In order to well deal with a linear bilevel programming problem what the upper-level's constraint functions being arbitrary linear form,Shi Chenggen gave an extended KT approach for linear bilevel programming.This paper analyzed the extended KT approach given by Shi Chenggen.A designed linear bilevel programming problem shows that the extended KT approach has different solutions from the general KT approach for some linear bilevel programming problems.It proposes an equivalent condition between the two kinds of KT approaches.The example shows that the equivalent condition proposed above is correct.