使用二次和几何不等式导出交互熵问题(英文)

MINIMUM DISCRIMINATION INFORMATION PROBLEMS VIA QUADRATICAL AND ARITHMETIC GEOMETRIC INEQUALITIES

考虑带二次约束和交互熵约束的最小二次规划和交互熵问题。基于二次和几何不等式的理论与性质。导出了上述两个规划原问题的对偶规划。进一步,由不等式中等式成立时的性质建立了两个原始-对偶规划的对偶定理和Kuhn-Tucker条件。

Considers quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratical inequality constraints and entropy inequality constraints of the density. The dual programs of two problems are derived by employing two simple inequalities,namely quadratic inequality and arithmetic geometric inequality. Furthermore,the duality theorems and related Kuhn-Tucker conditions for the two pairs of the prime-dual programs are also established by the properties of two inequalities if and only if the equalities hold.