多元函数条件极值的一种较精确的充分条件

›› 2017, Vol. 2 ›› Issue (12): 5-11.

多元函数条件极值的一种较精确的充分条件

（1. 广东省华立技师学院建筑与经济学部，广州511300；2.卡斯柯信号有限公司平台软件部，上海200071；3. 广州大学松田学院，广州511370；4.西南石油大学油气藏地质与开发工程国家重点实验室，成都610500）

收稿日期:2017-03-28 出版日期:2017-12-15 发布日期:2017-12-15
作者简介:张驰，硕士研究生，主要从事连续介质力学及最优化方法研究.

On a More Precise Sufficient Condition for Conditional Extreme Values of Multi-variable Functions

（1. Department of Civil Engineering, Guangdong Province Huali Technician College, Guangzhou 511300,China; 2. Department of Software Platform, CASCO Signal Ltd., Shanghai 200071, China;3. College Office, Guangzhou University Sontan College, Guangzhou 511370, China；4. State-Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China）

Received:2017-03-28 Online:2017-12-15 Published:2017-12-15

摘要/Abstract

摘要： 无条件极值的充分条件采用其目标函数的Hesse矩阵作为判别依据，但多元函数条件极值充分条件的判别矩阵却比较复杂。在分析了两种充分条件具有不同判别矩阵的原因的基础上，推导了条件极值的充分条件的判别方法，并采用一阶泰勒展开求解自变量增量间的关系式，得到了高维多约束状态下条件极值充分条件的一种较精确的判别矩阵。有助于理解两种充分条件的关联及差别，提供了一种寻找精确的条件极值的充分条件的判别矩阵的方法。

关键词: 拉格朗日乘数法, 多元函数, 条件极值, 充分条件, Hesse矩阵

Abstract: The sufficient conditions for unconditional extreme values are determined according to Hessian matrix, but the sufficient conditions for conditional extreme values are rather complex. Based on an analysis that the identification of the two kinds of sufficient conditions rely on different matrices, we derived a method of locating the sufficient conditions for conditional extreme values. By use of first order Taylor expansion in obtaining the relations among argument increments, a more precise matrix for determining the sufficient condition for conditional extreme values in high dimensions and with multiple constraints has been deduced. This helps a better understanding of the relationships and differences between the two kinds of sufficient conditions, and provides a means of finding a more precise sufficient condition for a conditional extreme value.

中图分类号:

O172.1

张驰，胡博，秦琴，钟海全. 多元函数条件极值的一种较精确的充分条件[J]. , 2017, 2(12): 5-11.

Zhang Chi, Hu Bo, Qin Qin, Zhong Haiquan. On a More Precise Sufficient Condition for Conditional Extreme Values of Multi-variable Functions[J]. , 2017, 2(12): 5-11.