IJPAM: Volume 23, No. 3 (2005)

ON FRITZ JOHN AND KKT NECESSARY CONDITIONS OF
CONSTRAINED QUASIDIFFERENTIABLE OPTIMIZATION

Zun-Quan Xia$^1$, Chun-Ling Song$^2$, Li-Wei Zhang$^3$
$^{1,2,3}$Centre for Optimization Research and Applications (CORA)
Department of Applied Mathematics
Dalian University of Technology
Dalian 116024, Liaoning, P.R. CHINA
$^1$e-mail: zqxiazhh@dlut.edu.cn
$^2$e-mail: mary_sohu@163.com
$^3$e-mail: lwzhang@online.ln.cn


Abstract.The Fritz John and KKT necessary conditions of constrained quasidifferentiable optimization in the sense of Demyanov and Rubinov
(1980), in the form of Demyanov sum of quasidifferential (1981), are presented and derived via Ekeland principle under the assumption of upper semi-continuity of the mapping of Demyanov sum of quasidifferential, that is weaker than the one given by Gao (2000). As an application, the optimality conditions of multi-objective optimization are also presented.

Received: May 28, 2005

AMS Subject Classification: 26A27, 90C26, 90C30, 49K99

Key Words and Phrases: nonsmooth optimization, quasidifferentiable functions, Ekeland principle, Demyanov difference (sum), multi-objective optimization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 3