IJPAM: Volume 5, No. 4 (2003)

SECOND ORDER OPTIMALITY CONDITIONS FOR
$\rm C^1$ MULTIOBJECTIVE OPTIMIZATION
PROBLEMS. SCALARIZATION

N. Gadhi$^1$B.P. 3536 Amerchich, Marrakech MOROCCO, H. Riahi$^2$
$^{1,2}$Department of Mathematics
Cadi Ayyad University
Marrakesh 40 000, MOROCCO
$^1$e-mail: n.gadhi@ucam.ac.ma
$^2$e-mail: h-riahi@ucam.ac.ma


Abstract.Multiobjective optimization is known as a useful mathematical model in order to investigate some real world problems with conflicting objectives, arising from economics, engineering and human decision making. In this work, we use a notion of approximate Hessian recently introduced by Jeyakumar and Luc [#!JL98-4!#] and some schalarization method to establish second order necessary and sufficient optimality conditions for constrained multiobjective optimization problems. Throughout the paper, the data are only assumed to be of class C$^{\text{1}}$ but not necessarily of class C$^{\text{1.1}}$.

Received: January 2, 2003

AMS Subject Classification: 90C29, 90C30

Key Words and Phrases: approximate Hessian matrix, recession matrices, second order optimality conditions, support functions, multiobjective optimization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 4