| 使用二次和几何不等式导出交互熵问题 |
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| 引用本文： | 朱德通. 使用二次和几何不等式导出交互熵问题[J]. 广西师范大学学报(自然科学版), 2003, 21(4): 53-60 |
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| 作者姓名： | 朱德通 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234 |
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| 基金项目： | National Science Foundation Grant of China(10071050),Science Foundation Grant of Shanghai Technical Sciences Committee(02ZA14070),Science Foundation Grant of Shanghai Education Committee(02DK06) |
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| 摘 要： | 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一对偶规划的对偶定理和Kuhn—Tucker条件。
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| 关 键 词： | 二次不等式 几何不等式 Kuhn Tucker条件 二次规划 交互熵问题 |
MINIMUM DISCRIMINATION INFORMATION PROBLEMS VIA QUADRATICAL AND ARITHMETIC GEOMETRIC INEQUALITIES |
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| Abstract. MINIMUM DISCRIMINATION INFORMATION PROBLEMS VIA QUADRATICAL AND ARITHMETIC GEOMETRIC INEQUALITIES[J]. Journal of Guangxi Normal University(Natural Science Edition), 2003, 21(4): 53-60 |
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| Authors: | Abstract |
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| Abstract: | 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. |
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| Keywords: | quadratic inequality arithmetic geometric inequality Kuhn-Tucker condition duality theorem entropy of the density |
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