IJPAM: Volume 6, No. 1 (2003)

NONSMOOTH MINIMAX PROBLEMS UNDER
V-$\rho$-$\sigma $-TYPE-I INVEXITY

S.K. Mishra$^1$, S.Y. Wang$^2$, P. Gupta$^3$, K.K. Lai$^4$
$^1$Department of Mathematics, Statistics and Computer Science
G.B. Pant University of Agriculture and Technology
Pantnagar - 263 145, Distt. Udham Singh Nagar, UA, INDIA
$^2$Institute of Systems Science
Academy of Mathematics and Systems Sciences
Chinese Academy of Sciences
No. A1 Nansijie Zhongguancun, Beijing 100080, P.R. CHINA
e-mails: sywang@iss02.iss.ac.cn, swang@mail.iss.ac.cn
$^3$Department of Mathematics
Faculty of Engineering and Technology
Raja Balwant Singh College, Agra 283 105, INDIA
$^{4}$Department of Management Sciences
Faculty of Business
City University of Hong Kong
Tat Chee Avenue, Kowloon, HONG KONG, P.R. CHINA
e-mail: mskklai@cityu.edu.hk


Abstract.In this paper, we introduce the class of V-$\rho$-$\sigma $-type-I invex functions and study a class of nonsmooth minimax programming problems. Necessary and sufficient optimality conditions and duality theorems for nonsmooth minimax programming problems are obtained under V-$\rho$-$\sigma $-type-I invexity assumptions.

Received: March 6, 2003

AMS Subject Classification: 46N10, 49J35, 90C46

Key Words and Phrases: minimax, V-$\rho$-$\sigma $-type-I invexity, optimality, duality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 1