Restricting the parameter set of the Pascoletti-Serafini scalarization

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‎A common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎This reformulation is called scalarization approach‎. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is considered‎. First, some difficulties of this scalarization are discussed and then removed by restricting the parameter set‎. A method is presented to convert a space ordered by a specific‎ ‎ordering cone to an equivalent space ordered by the natural ordering cone‎. ‎Utilizing the presented conversion‎, ‎all confirmed results and theorems for‎ ‎multiple objective optimization problems ordered by the natural‎ ‎ordering cone can be extended to multiple objective optimization‎ ‎problems ordered by specific ordering cones.