布尔函数最优连续化函数的信息论分析

不同形式的连续化函数在将组合优化问题转化为非线性连续最优化问题时对信息提取能力、对非线性规划问题的求解性质有很大的影响.利用信息论原理给出了布尔函数的连续化函数相对熵漏的概念,指出了它与Kull backLeibler距离之间的关系,给出了布尔函数的连续化函数是最优连续化函数的充分必要条件.这些分析结果可以直接推广到一般离散问题的连续化分析之中.

The Information Theory Analysis of Boolean Optimal Continuous Functions

Different continuous functions have a great influence on ability to collect information and property of solutions of the nonlinear programming problem. In the article, using the information theory principle, the authors give the definition of relative loss of entropy of Boolean continuous functions and point out the relationship between the loss of entropy and Kullback Leibler distance. At last, they give the full and necessary conditions those Boolean continuous functions are optimal. The conclusions to continuity analysis of general discrete problem can be directly extended.