Two Methods for Determining Properly Efficient Solutions with a Minimum Upper Bound for Trade-Offs

Abstract

This paper aims to investigate proper efficiency in multiobjective optimization. We suggest two nonlinear optimization problems to determine upper bound for trade-offs among objective functions. Based on these problems we introduce some properly efficient solutions which are closer to the ideal point. Weighted sum scalarization and Kuhn-Tucker conditions will be used to obtain these nonlinear optimization problems.