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.