Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Dau Xuan Luong and Tran Van An
Pages: [177] - [192]
Received Date: September 15, 2010
Submitted by:
In this paper, we apply the penalty function method to the multiobjective optimization problem, in order to transform a constrained problem, referred to as the original problem, into a sequence of simpler constrained or unconstrained problems, referred to as the penalized problems. We show that any cluster point of a sequence of weak efficient solutions of the penalized problems is a weak efficient solution of the original problem. Moreover, under certain assumptions on the feasible region D and the objective function f, we can show that every penalized problem has a weak efficient solution, and that a sequence of weak efficient solutions of the penalized problems always has at least one cluster point.
multiobjective optimization, nonlinear optimization, penalty function, weak efficient solution.
