Abstarct: In this thesis, we consider multiobjective optimization problems. The concept of proper efficiency is important scientifically and computationally in multiobjective optimization and the decision-making theory to avoid the answers with unbounded trade-off between the objective functions. A partial correction for Geoffrion's main definition is proposed preserves that common features of the proper efficient points. The proposed definition is applied for multiobjective optimization problems with infinite objective functions. The relations between the proposed proper efficient solutions and optimal solutions of the weighted sum and Tchebycheff-norm scalarization methods are investigated. We present new proofs and counterexamples that show the definition of proper efficiency in the sense of Geoffrion in general is not efficient for infinite objective functions. Since multiobjective optimization algorithms usually provide only an approximation solution, we analyze the concept of approximate Geoffrion's proper efficiency. We show that in the limit, approximate Geoffrion proper efficient solutions may converge to solutions having unbounded trade-offs. Furthermore, using a characterization baxsed on infeasibility of a system of inequalities, we examine the convergence properties of different approximate optimality concepts.We show that notion of approximate Geoffrion proper efficiency is only an approximation concept that shows the properties of a proper convergence.