IJPAM: Volume 22, No. 2 (2005)

$b$-SEMI-$E$-CONVEX FUNCTIONS AND
$b$-SEMI-$E$-CONVEX PROGRAMMING

You-fang Zeng$^1$, Jin-bao Jian$^2$, Qing-jie Hu$^3$
$^{1,2,3}$College of Mathematics and Information Science
Guangxi University
Nanning, Guangxi, 530004, P.R. CHINA
$^1$e-mail: zengyf@gxu.edu.cn
$^2$e-mail: jianjb@gxu.edu.cn
$^3$e-mail: hqj0525@hotmail.com


Abstract.In this paper, a new class of non-convex functions, called $b$-semi-$E$-convex (quasi-$b$-semi-$E$-convex, pseudo-$\bar{b}$-semi-$E$-convex) functions is introduced, and some of their basic characters are discussed. At the same time, some sufficient optimality conditions and duality theorems for the nonlinear $b$-semi-$E$-convex programming with inequality constraints are studied.

Received: June 28, 2005

AMS Subject Classification: 26A33

Key Words and Phrases: $E$-convex set, $b$-semi-$E$-convex function, $b$-semi-$E$-convex programming, optimality conditions, duality theorems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2