条件极值的充分条件与一类椭圆方程  

On Sufficient Condition of Conditional Extreme Value and a Kind of Ellipse Equations

作　　者：张驰 程功 钟海全[3] 黄华飞 ZHANG Chi;CHENGGong;ZHONG Hai-quan;HUANG Hua-fei(Department of Artificial Intelligence Ordering Platform, Chengdu Changyi Western Union Software Co. Ltd, Chengdu 610200, China;Institute of Urban Construction, Guangzhou Huali Science and Technology Vocational College, Guangzhou 511325, China;State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China)

机构地区：[1]成都长益西联软件有限公司智能订货平台部,成都610200 [2]广州华立科技职业学院城建学院,广州511325 [3]西南石油大学油气藏地质及开发工程国家重点实验室,成都610500

出　　处：《西南师范大学学报（自然科学版）》2019年第9期6-14,共9页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：通过分析无条件极值与条件极值的充分条件具有不同判别矩阵的原因,推导出条件极值充分条件的判别方法,得出其自变量增量间的关系式,得到了多维多约束状态下条件极值充分条件的一种更精确的判别矩阵,并举正反例说明判别驻点时可能出现的情况.有助于理解两种充分条件的关联及差别,提供了一种寻找更精确的条件极值充分条件的判别矩阵的方法.There is rarely discussion on sufficient condition of conditional extreme value of multi-variable function constraint to equalities in most mathematical analysis teaching materials, or with rather complex discussion instead, but conditional extreme value always follows unconditional extreme value tightly, which makes difficult to understand the relevance and difference between two kinds of discriminant matrices of sufficient conditions for students, or in mistake that both of discriminant matrices are in identity. To help students gasp the relevance and difference between both of them profoundly, understand sufficient condition of both problems of extreme value quicker and more comprehensive, sufficient conditions of unconditional and conditional extreme value have been discussed in detail, and different situations may encounter in distinguishing with various kinds of stationary points been explained by examples of validity and invalidity, this can help students understand the problem of extreme value quicker, more profoundly and comprehensively.

关 键 词：多元函数 条件极值 充分条件 HESSE矩阵 椭圆方程 

分 类 号：O172.1[理学—数学]