There has been numerous amount of studies on proper Pareto points in multiobjective optimization theory. Geoffrion proper points are one of the most prevalent form of proper optimality. Due to some convergence issues a restricted version of these proper points, Geoffrion proper points with preset bounds has been introduced recently. Since solution of any algorithm for multiobjective optimization problem gives rise to approximate solution set, in this article we study the approximate version of Geoffrion proper points with preset bounds. We investigate scalarization results and saddle point condition for these points. We also study the notion of approximate KKT condition for multiobjective optimization problem in general settings. Further, we discuss notion of approximate Benson proper point and develop KKT condition for the same.
Indian Institute of Technology, Kanpur India