Restricting the parameter set of the Pascoletti-Serafini scalarization

A common approach to determine efficient solutions of a multiple objective optimization problemý ýis reformulating it to a parameter dependent scalar optimization problemý. ýThis reformulation is called scalarization approachý. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is consideredý. First, some difficulties of this scalarization are discussed and then removed by restricting the parameter setý. A method is presented to convert a space ordered by a specificý ýordering cone to an equivalent space ordered by the natural ordering coneý. ýUtilizing the presented conversioný, ýall confirmed results and theorems forý ýmultiple objective optimization problems ordered by the naturalý ýordering cone can be extended to multiple objective optimizationý ýproblems ordered by specific ordering cones.