a quadratic approximation for multi-objective programming problems

In mmulti-objective optimization, several objective functions must be minimized simultaniously. these goals usually are in conflict with each other. so in most cases, there is no solution that optimizes all the objectives at the same time. therfore, the purpose of multi-objective optimization is to obtain nondominated points (instead of optimal solutions).the proposed method for approximating a nondominated set of multi-objective nonlinear programming is an extension of benson’s external approximation algorithm for multi-objective linear programming problems. we use the effective method of ”constructing a hyperplane separating an external point from the feasible set in the outcome space”. we want toapproximate the efficient border of the feasible set with a quadratic surface instead of a line, because this will increase the quality of approximation.