Necessary conditions for nonlinear suboptimization over the weakly-efficient set

The optimization problem of a nonlinear real function over the weakly-efficient set associated to a nonlinear multi-objective program is examined. Necessary first-order conditions for a suboptimal solution are proposed, assuming the convexity of the multi-objective program. Estimations of the optimal value are established and an algorithm for finding suboptimal solutions is proposed. The optimal value is approximated to any prescribed degree of accuracy using a weakly-efficient suboptimal solution.This work was done while the author was preparing his Ph.D. Thesis at the University of Melbourne, Australia. The author is thankful to Dr. B. D. Craven for his suggestions and helpful discussions and to Professor W. Stadler and the anonymous referees for their helpful comments and corrections.