Dual conditions characterizing optimality for convex multi-objective programs

Asymptotic necessary and sufficient conditions for a point to be a Pareto minimum, and weak minimum (proper minimum) for a convex multi-objective program are given without a regularity condition. It is further shown that, in the cases of weak minimum and single objective function, the asymptotic dual conditions reduce to nonasymptotic optimality conditions under Slater's constraint qualification. The results are applied to multi-objective quadratic and linear programming problems. Numerical examples are given to illustrate the nature of the conditions.