ϵ-properly efficient solutions to nondifferentiable multiobjective programming problems

AbstractWe introduce the concept of an ϵ-properly efficient solution and establish the equivalence between ϵ-optimality for a convex multiobjective program and ϵ-optimality for a related parametric (scalar) objective program. Using this equivalence, we establish the necessary and sufficient conditions for an ϵ-properly efficient solution of a nondifferentiable multiobjective objective functions subject to nondifferentiable convex inequality constraints, linear equality constraints, and abstract constraints