On cone characterizations of strong and lexicographic optimality in convex multiobjective optimization

Various type of optimal solutions of multiobjective optimization problems can be characterized by means of different cones. Provided the partial objectives are convex, we derive necessary and sufficient geometrical optimality conditions for strongly efficient and lexicographically optimal solutions by using the contingent, feasible and normal cones. Combining new results with previously known ones, we derive two general schemes reflecting the structural properties and the interconnections of five optimality principles: weak and proper Pareto optimality, efficiency and strong efficiency as well as lexicographic optimality.