On the mean value theorem for semidifferentiable functions

被引：1

作者：

Castellani, Marco ^{[2
,3
]}

Pappalardo, Massimo ^{[1
]}

机构：

[1] Univ Pisa, Dept Matemat Aplicata, Pisa, Italy

[2] Univ Aquila, Dept Sistemi, I-67100 Laquila, Italy

[3] Univ Aquila, Ist Econ, I-67100 Laquila, Italy

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2010年 / 46卷 / 04期

关键词：

Semidifferentiable functions; Mean value theorem;

D O I：

10.1007/s10898-009-9434-y

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：

The G-semidifferentiability concept was introduced in the reference Giannessi (J Optim Theory Appl 60:191-241, 1989) and it furnishes a general scheme for treating generalized derivatives. We prove that, in this context, it is possible to obtain a mean value theorem. By exploiting this result we deduce conditions for a function to be lipschitzian, C-decreasing or quasiconvex.

引用

页码：503 / 508

页数：6

共 4 条

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GIANNESSI, F .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1989, 60 (02) :191-241

[2] A Multifunction Approach to Extremum Problems Having Infinite-Dimensional Images. Necessary Conditions for Unilateral Constraints [J].

F. Giannessi ;

G. Mastroeni ;

A. Uderzo .

Cybernetics and Systems Analysis, 2002, 38 (3) :344-354

[3]

GIANNESSI F, 1998, ATTI SEMIN MAT FIS U, V46, P771

[4] CHARACTERIZATIONS OF QUASI-CONVEX FUNCTIONS [J].

LUC, DT .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1993, 48 (03) :393-406

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