摘要
本文针对经典优化问题中无约束函数极值判别法则的不定情况,首先对二元函数进行了研究,得出了更深入的判别法则,即将其转化为一个一元函数极值存在的判定问题;然后进一步将此法则推广应用到多元函数。文中的几个实例证明了该法则的可行性。
The uncertainty of the extremum problem of non-constrained functions is studied. The sufficient and necessary conditions for deciding whether a function has an extremum or not at a point where not all second-order and third-order partial derivatives of the function are equal to zero are given. It is proved that, if all the second-order partial derivatives but not all of the third-order partial derivatives are equal to zero,then the function has no extremum at the stationary point; and if not all the second-order partial derivatives are equal to zero, then the extremum problem of an n-element function will be converted into extremum problems of (n-l) ones of (n-r) -element functions, where r is the rank of Hessen matrix at a point.
出处
《华中理工大学学报》
CSCD
北大核心
1991年第3期107-111,共5页
Journal of Huazhong University of Science and Technology
关键词
无约束函数
极值
判别
不定情况
Non-constrained function
Extremum of function
Rule for ex- tremum judgement
Uncertainty
