Separate necessary and sufficient conditions for the local minimum of a function

被引：7

作者：

Huang, LR ^{[1
]}

机构：

[1] S China Normal Univ, Dept Math, Guangzhou, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2005年 / 125卷 / 01期

基金：

中国国家自然科学基金;

关键词：

optimization; necessary and sufficient conditions; directional derivatives; second-order directional derivatives;

D O I：

10.1007/s10957-004-1726-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper develops two necessary conditions for a local minimum of an arbitrary extended real-valued function (Theorem 2.2) and, quite separately, two conditions, each sufficient for such a function to have a strict local minimum (Theorem 2.3).

引用

页码：241 / 246

页数：6

共 50 条

[1] Separate Necessary and Sufficient Conditions for the Local Minimum of a Function
L. R. Huang
[J]. Journal of Optimization Theory and Applications, 2005, 125 : 241 - 246
[2] NECESSARY CONDITIONS AND SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM OF A FUNCTIONAL
ANTOINE, P
VANISEGHEM, F
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (10): : 523 - 526
[3] NECESSARY AND SUFFICIENT CONDITIONS FOR WEAK LOCAL MINIMUM
LUDERER, B
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1977, 57 (JUL): : 369 - 372
[4] NECESSARY AND ON SUFFICIENT CONDITIONS OF A LOCAL MINIMUM IN PROBLEM WITH CONSTRAINTS
LEVITIN, ES
MILYUTIN, AA
OSMOLOVS.NP
[J]. DOKLADY AKADEMII NAUK SSSR, 1973, 210 (05): : 1022 - 1025
[5] ON NECESSARY AND SUFFICIENT CONDITIONS FOR ABSOLUTE MINIMUM
ZAROSSKI.RI
[J]. DOKLADY AKADEMII NAUK SSSR, 1965, 163 (01): : 26 - &
[6] Necessary and sufficient conditions for a function to be separable
Viazminsky, C. P.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (02) : 658 - 670
[7] NECESSARY AND SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM .2. CONDITIONS OF LEVITIN-MILJUTIN-OSMOLOVSKII TYPE
IOFFE, AD
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1979, 17 (02) : 251 - 265
[8] NECESSARY AND SUFFICIENT CONDITIONS FOR A LOCAL MINIMUM .1. REDUCTION THEOREM AND FIRST-ORDER CONDITIONS
IOFFE, AD
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1979, 17 (02) : 245 - 250
[9] NECESSARY CONDITIONS FOR LOCAL PARETO MINIMUM
CALIGARIS, O
OLIVA, P
[J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1986, 5B (03): : 721 - 750
[10] THE NECESSARY AND SUFFICIENT CONDITIONS FOR LIPSCHITZ LOCAL HOMEOMORPHISM
FAN, XL
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1992, 13 (01) : 40 - 45

← 1 2 3 4 5 →