Fritz John’s type conditions and associated duality forms in convex non differentiable vector-optimization

Necessary and sufficient conditions of the Fritz John’s type as well as wolfe’s type duality for convex non differentiable constrained multicriteria optimizaton problems have been studied by others under a rather strong constraint qualification. The paper first notes that under the latter constraint qualification, every Pareto-optimal point is in fact a proper Pareto-optimal point in the sens presently commonly accepted. Furthermore, it shows that with a weaker constraint qualification, similar necessary and sufficient conditions and duality results as above still hold for proper Pareto-optimality. The paper also considers a dual derived from the Fritz John saddle point type problem.