n元函数局部极值存在的一阶充分条件  

First⁃Order Sufficient Conditions for Existence of Local Extremums of Multivariate Functions

作　　者：黄正刚 HUANG Zhenggang(College of Science,Chongqing University of Technology,Chongqing 400054,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《应用数学和力学》2020年第6期687-694,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(50573095)。

摘　　要：提出了n(n≥1)维欧氏空间中,相对经典无约束最优化问题更一般情况下,局部极值存在的统一的一阶充分条件,解决了最优化领域至今没有这一结论的困难,证明了一元函数局部极值存在的一阶充分条件是它的特殊情况.通过具体例子说明了该文结论可以消除经典的多元函数局部极值存在的二阶充分条件的缺点,最后在拟凸、拟凹假设下证明了该结论还是n元函数局部极值存在的充分且必要条件.The unified 1st⁃order sufficient condition was proposed for existence of the local ex⁃tremums of n⁃variable functions,in a case more general than classical unconstrained optimiza⁃tion ones.The difficulty of no such 1st⁃order sufficient condition in optimization theories was solved.Moreover,the 1st⁃order sufficient condition for 1⁃variable functions was proved to be a special case of the results.The work can eliminate the shortages of the 2nd⁃order sufficient con⁃ditions for existence of local extremums of classical multivariate functions,and the result is both necessary and sufficient under the assumption of quasiconvexity or quasiconcavity.

关 键 词：局部极值 一阶充分条件 二阶充分条件 拟凸 拟凹 

分 类 号：O224[理学—运筹学与控制论]